Daily Chess Improvement: Attacking Chess Tactic!

This was one of the chess puzzles from 2018 SPFGI

It is white to move. There is nothing more frustrating in chess than to think you are about to win the chess game only to let the opponent escape. It seems that the black king has escaped in this chess position. Is there a way to close it out?

No. 1-1
Juan Macias
Juan Macias
  1. Rxh6+ Kh6 2. Qh8+ Kg6 3. Qh5+ Kf6 4. Qg5#