Rook Endgame: Converting the Outside Passed Pawn

When the enemy pieces are each tied to a defensive job, count the rest of the board as if those pieces were gone. Here the pawn on b6 holds the black king on the queenside while the rook is tied to the seventh rank defending h7, so neither piece can come to the kingside: you are effectively a king, rook and pawn against a single pawn there.

Attack where you have the extra force. The black king is glued to b7 and a6, blockading the b6-pawn from the front and the side, and the rook cannot leave the seventh rank without dropping h7, so your king walks over: Kh5, g5, Kh6. Do not hurry the b-pawn; its value is the paralysis it creates, not its promotion.

Cash in and queen. Sooner or later Black grabs the b-pawn, but that costs him the h-pawn, and your g-pawn runs with the king ahead of it. The checks from behind are answered with the Lucena bridge, the rook shielding the king on the fourth rank.

In this drill the defender will hold the blockade as long as it can and then check. Keep the king in front of the pawn, build the bridge, and promote.