Before racing, check the queening squares: if your queen would arrive without check and without a skewer, look for a slower but decisive plan.
Change one detail from the previous lesson: the black king is on a7 instead of b8. Now the natural race fails. 1.h6? a3 2.h7 a2 3.h8=Q a1=Q and White's queen on h8 does not check a7; even the long diagonal skewer h8-a1 is blocked by White's own king on e5. The game is a draw.