The ball weighing 200 g is moving at 20 m/s. It hits the ball weighing 650 g which is assumed to be stationary. Using the law of conservation of momentum, the initial momentum of the two balls is equal to the final momentum. Initially , the momentum of the 200 g ball is 0.2*20 = 4 kg*m/s, the momentum of the 650 g ball is 0. As the velocity of the 650 g ball after collision is not given it is assumed to be V. After the collision, the momentum of the 650 g ball is 0.650*V. Equating initial and final momentum gives the final momentum of the 200 g ball as 4 - 650*V'.
From the law of conservation of energy, the kinetic energy initially is 80 + 0. After collision is remains the same or 80 = (4 - 650)/200 + 650*V^2.
Both momentum as well as energy of the system made up of the two balls remains constant before and after collision.