For this one, you don't apply Lenz's Law - at least not in my approach.
Initially the voltage of X is positive doesn't that mean that current is initially flowing at Y and electrons are flowing to X?For this one, you don't apply Lenz's Law - at least not in my approach.
In fact, you apply the Left Hand Curl Rule (LHCR). As the CRO shows a wavy voltage (not a straight line), you can deduce that this is AC and not DC. So you can eliminate A and C because they have a split ring commutator which is characteristic of DC.
Now look at the X and Y positions in the options and your AC voltage graph. Initially, the current is positive, so that means that current is flowing into X (i.e. current is flowing in the direction of the arrow at X in the options). This means current is travelling out of the page in the coil, so you point your left thumb towards you. You'll notice that the curve of your hand is clockwise - and this is the direction the handle must be rotated in.