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Try this IF( ISPICKVAL( [In_Form__Risk_Assessment__c].Risk_present_MH__c , "No" ) , "No risk" ,

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) < 8, "Low",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 8, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 9, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 10, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 12, "Medium",

IF( CASE([In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) > 12, "High", "" )))))))

IF( ISPICKVAL( [In_Form__Risk_Assessment__c].Risk_present_MH__c  , "No" ) , "No risk" ,

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) < 8, "Low",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 8, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 9, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 10, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 12, "Medium",

IF( CASE([In_Form__Risk_Assessment__c].Likelihood_mental_health__c   , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) > 12, "High", "" )))))))

Try this IF( ISPICKVAL( [In_Form__Risk_Assessment__c].Risk_present_MH__c , "No" ) , "No risk" ,

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) < 8, "Low",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 8, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 9, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 10, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 12, "Medium",

IF( CASE([In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) > 12, "High", "" )))))))

Try this

IF( ISPICKVAL( [In_Form__Risk_Assessment__c].Risk_present_MH__c  , "No" ) , "No risk" ,

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) < 8, "Low",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 8, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 9, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 10, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c  , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 12, "Medium",

IF( CASE([In_Form__Risk_Assessment__c].Likelihood_mental_health__c   , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c  , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) > 12, "High", "" )))))))
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Naga
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From line 3 to 6 where you are checking if the values are equal to a number, there should be two equals instead of one.

Try this IF( ISPICKVAL( [In_Form__Risk_Assessment__c].Risk_present_MH__c , "No" ) , "No risk" ,

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) < 8, "Low",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 8, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 9, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 10, "Medium",

IF( CASE( [In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) == 12, "Medium",

IF( CASE([In_Form__Risk_Assessment__c].Likelihood_mental_health__c , "Very likely (5)", 5, "Likely (4)", 4, "Possible (3)", 3, "Slight (2)", 2, "Very unlikely (1)", 1, 0) * CASE( [In_Form__Risk_Assessment__c].Severity_of_impact_mental_health__c , "Critical (5)", 5, "Major (4)", 4, "Significant (3)", 3, "Minor (2)", 2, "Insignificant (1)", 1, 0) > 12, "High", "" )))))))