bad puzzle

today i played a bad puzzle.

here it is http://en.lichess.org/training/8583 here i played f4 which wins quicker than h4

f4 does not win at all after exf4

36. f4+ exf4 and what then?

then 2.h4, and 2...kh5 meets mate at 3.rd5# or if black does 2...kf6 then white does rf7#

2.kh5 3.rd5 kg4
2.kh5 3.kf6 ke5
2.kh5 3.kg4 (you didn't even mention this)

You are really misscalculating this.

Pro tip: If you think that something else may work you can start game vs stockfish lvl 8 bot in that situation and do you move. Machine will prove you wrong.