This isn't the type of position that features in a puzzle where White has a mating attack or quick win of a piece. It's a hard slog!
Deep computer analysis suggests a line like this 47. Kxg6 Rg4+ 48. Kf5 Rc4 49. Ke6 Rc1 50. Kd5 a4 51. Ra7 Rd1+ 52. Ke6 Re1+ 53. Kf5 Rf1+ 54. Kg5 Rf6 55. Ra8+ Kh7 56. Rxa4 when Black's hopes of counterplay with the a pawn are taken away.
If I were you I would play Kxg6, then if possible deliver mate by taking rook to the eight rank.
