As Phil W mentioned, you cannot filter long text fields in SOQL. You can vote for the idea to allow this.
You didn't really specify the context for this. If it's a trigger context, then you already have the records. I'd be worried about your query size if you have millions of accounts and no real way to narrow down which ones you want to check the Notes of in a SOQL query. If you have some other fields you can utilize and are sure you could narrow it down then it should work fine.
Once you have a list of accounts, it's easier. You can check how many matches you find to your substring in a given long text area field with countMatches() as below:

Specific to your scenario, a simple for loop like this would work:
for(Account acc : accountList){
if(acc.Notes__c.countMatches('04/06/2020') == 2){
//do whatever you need to do
}
}
I'm not sure how you're building what date to find, but you'd want to make it dynamic (based on today, etc) or a label that you can change when you want to run and check. As mentioned above, depending on the context (trigger execution, scheduled job), be aware of any SOQL limits with the returned rows.
Notes__c
, Text Area?countMatches()
in apex