A cursory look at White’s attacking options turns up Rxb7, taking a pawn for free. But even when you have a simple capture available it's worth asking whether you might have something still better. Standard procedure for the purpose, of course, is to experiment with any checks you can give; safe checks with your queen are especially important because they may in effect give you a free move. Here White has one in Qd3. It forces Black to move his king to the back rank or play g7-g6. Either way, ask what White could do next. Answer: fork Black’s rooks with Qd7, taking one or the other of them a move later.
Of course another way to see this is by scouting for loose pieces on the board. Two loose pieces, as Black has here—and on the same diagonal, no less—beg to be forked. You see that your queen needs two moves to get to the forking square; so you ask whether you can make the first move a check that will keep Black busy. This leads to Qd3 as a transitional move.
A natural mental sticking point here is to start looking at the check Qd3 and then give up when you conclude that you then have no good follow-up against Black’s king. The trick is to be flexible enough in your thinking to move from looking at checks against the king to looking at follow ups against other pieces. In this case the power of the check Qd3 isn't that it forces Black’s king to change squares; it's just that it gives White a way to move his queen across the board while denying Black a chance to respond. Anyway, if you are conscious of the two loose rooks in this position you won’t overlook 2. Qd7, because you will be thinking all the time about how to get at them.