The square rule is the defender's side of the pawn race, and it replaces move-counting with a single glance: draw an imaginary square from the pawn to its promotion square, as wide as it is tall. If your king can step INSIDE that square on its move, it catches the pawn. Outside, the pawn queens and nothing can be done.
The trap is that the square shrinks every time the pawn advances, so a king that dawdles for one move can find the boundary has moved past it. When a pawn starts running, check the square immediately, and take the diagonal path toward it, a king moving diagonally covers two directions at once for free.
White's h-pawn is running. The square runs from h5 across to e5 and up to the 8th rank.
Only one king move still catches the pawn. Find it.