find the right move

Nf2+

The answer is Qb8+, Rxb8, Nf2#.

1. Qg1+ hxg1=B, h8=Q Qh6, Qxh6+ Bh2, Qxh2# 

Whoops, I meant Qg1+, Rxg1, Nf2#. I flipped the board.

The board is weird...

1.Dg1+ hxg1=D 2.h8=D+ Dh6 3.Dxh6+ Dh2 4.Dxh2#

who is to move or did I miss something?

B3 to D4? 

Qg1+, Rxg2, Nf2#

king cant take

If Qg1+, Black will just take it with the Pawn.

You should set the board up with the ranks and files correctly oriented.

 It's Qg1+  hxg1=Q (if Rxg1 then Nf2#)

      h8=Q+  Qh2

      Qxh2#

     If black underpromotes to a Knight, then then: h8=Q+  Nh3

                                                                                Qxh3#

     More interesting would be coming up with a game that could result in this position.