A simple formula that will do it is where I have 2 custom fields both of Date data type, Start_Date__c and Target_Test__c. You could change the <> to a >= to make it greater than or equal to the date.
Target_Test__c <> CASE( MONTH(Start_Date__c) ,
1, DATE(YEAR(Start_Date__c),10,31) ,
2, DATE(YEAR(Start_Date__c),11,30),
3, DATE(YEAR(Start_Date__c),12,31),
4, DATE(YEAR(Start_Date__c)+1,1,31),
5, DATE(YEAR(Start_Date__c)+1,02,28),
6, DATE(YEAR(Start_Date__c)+1,03,31),
7, DATE(YEAR(Start_Date__c)+1,04,30),
8, DATE(YEAR(Start_Date__c)+1,05,31),
9, DATE(YEAR(Start_Date__c)+1,06,30),
10, DATE(YEAR(Start_Date__c)+1,07,31),
11, DATE(YEAR(Start_Date__c)+1,08,31),
12, DATE(YEAR(Start_Date__c)+1,09,30),
DATE(YEAR(Start_Date__c),10,31))
1, DATE(YEAR(Start_Date__c),10,31) , 2, DATE(YEAR(Start_Date__c),11,30), 3, DATE(YEAR(Start_Date__c),12,31), 4, DATE(YEAR(Start_Date__c)+1,1,31), 5, DATE(YEAR(Start_Date__c)+1,02,28), 6, DATE(YEAR(Start_Date__c)+1,03,31), 7, DATE(YEAR(Start_Date__c)+1,04,30), 8, DATE(YEAR(Start_Date__c)+1,05,31), 9, DATE(YEAR(Start_Date__c)+1,06,30), 10, DATE(YEAR(Start_Date__c)+1,07,31), 11, DATE(YEAR(Start_Date__c)+1,08,31), 12, DATE(YEAR(Start_Date__c)+1,09,30), DATE(YEAR(Start_Date__c),10,31))
If you need the Specific Date returned then I would think using a formula field with Date return type and the formula from 'CASE..' onwards would work better than manual entry.
