One of the best questions in probablity. The anwer is c and not b.I really can’t understand why we are subtracting 2 from 2^6 in the number of choices for birthdays.

That is the case when birthdays of 6 people lie in one month.
Question asks to find for “exactly” two months. There may be case when birthdays lie in 1 month, say January for example. 
ATB