Assuming the white pieces started off at the bottom of the board, white can check mate the Black king in 4 moves considering the following optimal moves on both sides
F8 to E6 ( White Horse ) 1st move
H7 to H6 ( Black Pawn )
F7 to F8 ( White Pawn converted to Queen ) 2nd Move ( Check )
H8 to H7 ( Black King to avoid Check )
C4 to D3 ( White Queen to check ) 3rd move
G7 to G6 ( Black Pawn to avoid Check )
F8 to G7 ( White Queen to check the King ) ( has Support of Horse at E6 ) 4th Move CHECK MATE !