this is the easiest way to do it i think. the other way i can think of is to do all the combinations manually, that is,

P(getting heads with first coin, tails with second, heads with third, tails with fourth) + P(heads with first coin, heads with second, tails with third, tails with fourth) + .....

and try to make sure you get all combinations of two heads and two tails, which would be a pain, Bernoulli Trials is definatley the way to go here, which is what you did.

Maybe Soroban can come up with some other way, he's somewhat of a genius with probability