Highly doubt there would be an error in VCAA solutions. If something's wrong they will revise it.
Okay, so when the switch is closed, the current is increasing, creating an increasing magnetic field. The field's direction points towards the left. At the second coil, the direction of the magnetic field is also pointing towards the left. The current induced in the coil will be such that it opposes the change, hence we want to induce a field towards the right. Creating a field pointing towards the right requires a current to flow from Y to X.
The current only flows momentarily, as once the current maintains a steady value there will no longer be any change in flux and hence no induced current.
So the answer is B.