Work Step by Step
The wire has a current in the leftward direction, which means the magnetic field that it creates wraps around the wire such that it goes into the page when passing through the loop. When the wire is being pulled downward, the strength of the magnetic field through the loop decreases since the wire gets further away from the loop. Thus, we can imagine that there is an "induced" magnetic field that is in the same direction as the magnetic field created by the wire. Think of it this way: when the wire is stationary, the magnetic field throughout the loop is constant. When the wire is stationary, no current flows through the loop. Once the wire starts moving, the magnetic field of the wire decreases with distance, and the wire gets further away from the loop so the magnetic field through the loop must decrease. The "induced" magnetic field wants to keep the overall magnetic field at what it was when it was stationary, so to make up for the lost magnetic field due to the wire from moving far away, it points int he same direction as the magnetic field created by the wire so that it strengthens the overall magnetic field through the loop. Because the "induced" magnetic field is into the page, doing a simple right-hand curl (with our thumb pointing into the page), will yield a clockwise direction. Thus, the direction of the induced current is clockwise.