number of Saturdays between those 2 dates. Create formula field

FLOOR(( End_Date__c -  Start_Date__c )/7)

+

IF(OR (WEEKDAY(Start_Date__c )=7, WEEKDAY(End_Date__c )=7, WEEKDAY(Start_Date__c )>WEEKDAY(End_Date__c )),1,0)


If you want the number of Sundays:

FLOOR(( End_Date__c -  Start_Date__c )/7)

+

IF(OR (WEEKDAY(Start_Date__c )=1, WEEKDAY(End_Date__c )=1, WEEKDAY(Start_Date__c )>WEEKDAY(End_Date__c )),1,0)


This is easily changed for any day of the week. You only need to change the "WEEKDAY" number (1 for Sunday, 2 for Monday, 3 for Tuesday, etc) in this part:

WEEKDAY(Start_Date__c )=1, WEEKDAY(End_Date__c )=1

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