Conservation of momentum: total momentum before = total momentum after
Momentum = mass x velocity
So before the collision:
4kg x 8m/s = 32
1kg x 0m/s = 0
32+0=32
Therefore after the collision
4kg x 4.8m/s = 19.2
1kg x βm/s = β
19.2 + β = 32
Therefore β = 12.8 m/s