Kh4 Bf5 then Kh5 is black's only move then white would probably play something like Kf6.. and then Kh4 is black's only move and then you can play Be6 Kh5 (once again only move) Bg3.. and you push the black king neatly up the board to the corner and mate him..
On the sixth move the mentor wants me to move Bf4, a move I discounted because it leaves the light square bishop hanging after Kh4. On the next step the mentor says that:
"Note that 6...Kh4 7.Bf5 would leave the Black king right where White wants it."
Wouldn't Kh4 secure a draw in this position? What am I missing?
I don't see it. Doesn't 6...Kh4 7.Bf5 leave both bishops hanging? The white king is too far away to save either of them. Here's a screenshot: