Black's missing a knight, a bishop, and a rook...all of which needed to be captured by the promoting pawn to get to the h file. Promoting on a-c would trap the rook or force the king to move, promoting on d or f would force the king to move, and g would requre the pawn getting to the h file and making a 4th capture back to g8.
exd6 had to happen to let the bishop out, and dxe6 had to happen before that to let the rook in, so d7 cannot be the promoted rook.
It could be either of the other 2, though, if the c1 bishop was captured on its own space and white's knight was captured on d6. If this was supposed to say that neither king has been put in check instead of just not moving, or if white's other knight is supposed to be on the board somewhere, it'll force the c1 bishop to be free to move to d6, which would trap a1 and require the promoted rook to be on h8.
Knowing that neither King has yet moved in this game, deduce which of the Three White Rooks is the promoted piece.