The first lesson of my Step 2 class is about "piece activities". It is a critical topic. The numbers of pieces are not determining factor, instead activities of pieces are. Here black is up two pawns, but they are not useful.
Look at black pieces. Bishop only has one place to go, c5. Queen can only go to g8, while Rook and King can go to g8 and h7. All threes pieces are fighting for these two available squares. The King is blocking the g-file. It will take three moves for black Queen or Rook to get out. But black doesn't have the luxury for three free moves.
On the opposite, white pieces are all active and ready to attack. King is safely tucked on b2. Even two isolated f pawn and h pawn are useful. They block black pawns and restrict black space.
Now how to start the attack?
Qg3+ looks very nice, but after Kh7, we can't go to Qg6+ because of f7 pawn, no matter how much we desire for that square. So checking is premature and not helping us. In fact it helps black because black has to move the King anyway to move out his Queen or Rook. So we should not check now.
Look at the 7th rank. Although there are lots of pieces on the rank, this is in fact the weakest rank for black. The Bishop is only protected by Queen, and the f7 pawn by Queen and King. If we can't attack the King, we attack pieces or weak spots. Rd7 is a nature move. Notice, black Bishop can't move to Bc5, because f7 pawn will be pinned by our Rook and our earlier plan will lead to a mate.
So our twofold attack will land us a Bishop. After we get the Bishop in the next move, we will attack the f7 pawn twofold. If black King moves away from g7, we will take the pawn and get the Queen. If the King stays, we still threat checkmate with our original plan, and also Re8 to trap the Queen. Black will get into Zugzwang in the end.