The kinetic energy of the compound system immediately after the collision can be found from the fact that:

The conservation of momentum yields the final velocity of the system immediately after the collision, hence the kinetic energy of the compound system.

Explanation:

If we are talking about a compound system, then we know for a fact that the system is in completely inelastic collision, because this is the case when objects are stick together after the collision.

In completely inelastic collisions, the momentum is conserved but the kinetic energy is not.

However, since there is only one mass after the collision, the equation comes from the conservation of momentum will be enough to find the final velocity of the compound system, therefore the kinetic energy of the compound system.