Topic: Collisions
Concepts: 1D elastic collision, CM frame

Solution:

Initially, mass $m$ is moving at $12\,\mathrm{m/s}$ towards the $4\,\mathrm{kg}$ mass at rest.

We go to the CM frame (moving at $v_{\text{CM}}$):

Recall the total linear momentum $p_{\text{tot}}=M_{\text{tot}}v_{\text{CM}}$ so $p_{\text{tot}}=0$ in the CM frame (since the CM is at rest by definition). Then after an elastic collision, the velocities just flip directions: The speeds of both objects stay the same which conserves energy. Flipping velocities changes the sign of the momentum. But $-p_{\text{tot}}=p_{\text{tot}}$ since $p_{\text{tot}}=0$ so momentum is also conserved.

Lastly, we go back to the ground frame (adding velocity $v_{\text{CM}}$ to the right on both objects):

We are given that mass $m$ moves to the left with velocity $6\,\mathrm{m/s}$. Thus,

so the answer is B.