In the diagrams below, a strong bar magnet is moving towards solenoid-2 from solenoid-1 with velocity $v$. The magnet is oriented with its North pole (N) facing solenoid-2 and South pole (S) facing solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:

According to Lenz's Law, the induced current will create a magnetic field that opposes the change in magnetic flux.For Solenoid-1: The South pole (S) of the magnet is moving away from it. To oppose this, solenoid-1 will develop a North pole at its right end to attract the receding S-pole. Using the right-hand thumb rule, the current must flow in the direction $AB$.For Solenoid-2: The North pole (N) of the magnet is moving towards it. To oppose this, solenoid-2 will develop a North pole at its left end to repel the approaching N-pole. Using the right-hand thumb rule, the current must flow in the direction $DC$.Thus, the directions are $AB$ and $DC$.