Acoin is flipped three times. how does p(h, h, h) compare to p(h, t, h)?

P(H,H,H)=P(H,T,H)

This is classical probability, so the probability of an event is the number of "favorable" events over total events.

The total number of events, by the counting principle, is 2^3=8.
The total number of events remains the same for P(H,H,H) and P(H,T,H), as you're still flipping 3 coins with two sides.

For P(H,H,H) the favorable event is (H,H,H) so 1, for P(H,T,H) the favorable event is (H,T,H) also one.

Conclusion:

P(H,H,H)=P(H,T,H)=1/8