puzzle white to play

That is one line
After b6 Black can go Rg4+ kc3 but you have to go back with the rook and get to the line above or play Bd8 Bb8+ Bc7 Bxc7#

Something appears to wrong with the diagram as white has dual ways to win during the solution. If we get the right diagram there may be some new surprises.
The main problem with b6 seems to be Rg4 followe by Ke5, with a total escape and seemingly no way to promote.
Message #3 correctly points out the problem with Bb8, which looks like the most enticing move, almost forcing a promotion.
the most practical move seems to be Bc5 or h7, but it's not a satisfactory puzzle answer