How can white checkmate black in this chess puzzle?
Assuming white is moving up the board in the position as shown,

1.Rxg8+ Kh7
2.Rxg7#

BTW, the usual notation for Knight is N, not H.

You can also use online tools to make better pictures (and to produce more easily-shareable notation for the board).

For example https://www.365chess.com/analysis_board.php

For instance, your puzzle in FEN is

RR4bk/1B1ppnp1/5PnP/2pN2P1/1b6/2P2pp1/1P1P1p2/7K w - - 0 1