The coil A is made to rotate about a vertical axis as in figure. No current flows in B if A is at rest. The current in coil A, when the current in B (at t = 0) is counter clockwise and the coil A is as shown at this instant, t = 0, is

In this case, the direction of the induced electromotive force/induced current is determined by the Lenz's law. According to the Lenz's law, the direction of induced emf or current in a circuit is such that it oppose, the cause that produces it. This law is based upon law of conservation of energy.
When the current in coil B (at t : 0) is counterclockwise and the coil A is considered above it. The counter-clockwise flow of the current in coil Bis equivalent to North Pole of magnet and magnetic field lines are eliminating upward to coil A. When coil A starts rotating at t = 0, the current in coil A is constant along clockwise direction by Lenz's rule.