How many two move checkmates exist? I am well aware that Fool's Mate exists. But how many two move checkmates exist in total?
I agree with the previously-given answer from Matthew Liu (please give it the checkmark), but I’ll add the standard notation of the solutions since you ask:

1.f3 e5 2.g4 Qh4#

1.f3 e6 2.g4 Qh4#

1.f4 e5 2.g4 Qh4#

1.f4 e6 2.g4 Qh4#

1.g4 e5 2.f3 Qh4#

1.g4 e6 2.f3 Qh4#

1.g4 e5 2.f4 Qh4#

1.g4 e6 2.f4 Qh4#