Since the first coin toss has no bearing on whether the game will end on the fourth toss, we can ignore it. Our only consideration is what is the probability that the second throw will be heads, the third throw tails, and the fourth throw heads?

There is a 1/2 chance that the second throw will be heads.
There is a 1/2 chance that the third throw will be tails.
There is a 1/2 chance that the fourth throw will be heads.

The chances that all three will occur is (1/2)^3 or 1/8.