By way of transition, consider now a case where the pinned piece, rather than the screened piece, can break the pin by making a threat. Do you see the pin that is troubling Black? His knight on e2 cannot move without exposing his rook, which is loose, to capture by White. And if it were White’s turn he would win a piece, as the pinned knight is attacked twice and protected just once. But it’s Black’s move, so look for an offensive option with one of the pieces that is party to the pin; perhaps it can create a sufficient distraction to allow both pieces to escape.
Can either piece give check? No. Can either attack a loose White piece? No. What else is there? Always be aware of the enemy king: its constraints and any pressure you are exerting against it—and especially any pieces currently attacking any squares adjacent to it, for that is what mate threats are made of. Here Black’s other rook on b6 bears down on the b-file next to White’s king. A move that adds another attack against the b1 square—say, Nc3— would add to the pressure on the king, because it would put Black in position to play Rb1 with protection. That threat doesn’t quite seem decisive here because White also protects b1 with his rook now on e1. But an idea comes into view: if Black plays Nc3, he invites White to execute the pin with RxR—which is fine, because then Black would mate with Rb1. White can decline RxR, of course, but he has to do something with his e1 rook because it would be under attack. Probably he would move it to c1, which again suits Black fine; for now the pin is broken.
Notice, then, all that Nc3 does: it’s a discovered attack, unmasking a threat against White’s rook by the pinned piece while also launching a fresh threat against the mating square b1. White can extinguish both threats with Rc1, but by then Black has escaped trouble.