I had a hard time with this one, though I shouldn't have. How will you do?
1N1K4/2R5/3ppP2/1P1kpb2/2n4P/2P1PPB1/2npp1NQ/4b3 w - - 0 1
At first I got a lot of mates in 5. Then I guessed how to mate in 4.
1.Qh1 d1=Q2.e4+ Bxe43.Ne3+ N2xe34.fxe4#
Ra6, d1 (Queen promotion)
Na6, d1 (Queen promotion); Rc6, Bxg3; Qxg3, Nxe3; Nc7+mate
1.Qh1 N2Xe32.Na6 Nc23.Rc6 e44.Nc7#
1.Qh1 N4xe32.Nd7 Nc43.f7 e44.Nf6#
1.Qh1 Be42.Nf4+ exf43.fxe4+ Ke54.Nd7#
Will White MATE IN 4 when 1. Ra6, e4?
Will White MATE IN 4 when 1. Qh1, e4?
After 1.Qh1 e4 then 2.Nf4 Ke5 3.Nd7#, so not in four, but in three which satisfies the puzzle's stipulation which is mate in no more than 4.
The last line is the key one for 1.f7. 1.f7 Bg3 2.Nd7 e4, and I could never find a mate in 4, but only mate in 5.