How many possible two-move checkmates are there?

Question

Yes, I am well aware that Fool's Mate exists. But how many other possible two move checkmates exist in chess?

Answer 1

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#

Answer 2

8 different ways. 2 different ways for f3/f4. 2 different ways for e6/e5. 2 different ways for changing the move order between g4 and f3/f4.