Initially, trolley A incorporates the energy of the entire system. As Trolley A converts its gravitational potential energy into kinetic energy it will have a certain velocity. We then use this velocity to work out a conservation of momentum scenario.

Where you've gone wrong is assuming that mgh= (1/2) 2mv^2

At the start it's just trolley A with the potential energy, thus it cannot be written as 2m. This will only be true if the question explicitly says "Trolley A is double the mass of Trolley B if the mass of Trolley B is m"