This is a bit tricky -- in the first part we dropped the ball from 2.0 meters, but after it bounces, it only goes up to 1.1 meters. This means the bounce itself did not conserve energy... So for now we aren't going to worry about what's going on during the bounce itself, just what happens before (which you did in part a) and what happens after (what you are to do right now.)
So what we know is how high it went after the bounce -- what we need to find out is what velocity it needed to reach a maximum height of 1.1 meters.
The easiest way to think of this is to pretend the ball is thrown upwards from the ground, reaching a maximum height of 1.1 meters -- alternatively you could be sneaky and pretend the ball is being dropped from 1.1 meters, and see what the velocity is right when it hits the ground... You'd get the same magnitude, just the direction would be opposite...
(the positive root because the ball is going up)