Answer
It will not rotate.
Work Step by Step
Since the string and the pulleys are massless and frictionless, the forces exerted on both sides are equal and the two blocks remain stationary, and hence the pulley will not rotate.
You can argue that the net force exerted on both blocks is zero and yet they can move at a constant speed up or down, but what makes them do that since the string is massless?
Yes, in the real world the right block will move down while the left one will move up since the right block has a longer segment of the string (and hence longer weight) than the other.
But the author here told us that the string is massless, so the weights on both sides are exactly the same and hence no motion occurs.
