A6 kg ball moving west at 4 m/s collides with a 4 kg ball moving east at 3 m/s. what is the velocity (magnitude and direction) of the 4 kg ball after the collision if after the collision the 6 kg ball comes to a stop?

This is a conservation of momentum problem. We know the momentum initial=momentum final.
Momentum= mass* velocity
Ball 1 has a mass of 6kg and initial velocity of 4and final velocity of 0
Ball 2 has a mass of 4 and a initial velocity of -3 and a final velocity of x
Notice i set west as postive velocity and east as negative.
Momentum initial= ball 1 momentum(inital)+ ball 2 momentum initial.
= 6kg *4 m/s+ 4kg*-3m/s= 12kgm/s
Momentum final = 6kg*0m/s + 4kg*x
Since final = inital
12= 4x
X=3 m/s
Since it is positive that means 3 m/s west