The ball with a mass 0.25 kg is rolling towards a person at 6 m/s. It is kicked by the person which results in the ball moving in the opposite direction at 14 m/s. The force applied by the person for this to happen lasts for 0.2 seconds.
Let the force with which the ball is kicked be F. The initial velocity of the ball is 6 m/s towards the player. After it is kicked the velocity is 14 m/s away from the person. This gives the net change in velocity as 14 + 6 = 20 m/s. The change in velocity occurs over a time period of 0.2 seconds. The acceleration that causes this is 20/0.2 = 100 m/s^2. As the mass of the ball is 0.25 kg, the force applied is 0.25*100 = 250 N.