Recall the following formula for a 1D elastic collision in which particle 2 is initially at rest:
$\begin{align*}v' = \frac{m_1 - m_2}{m_1 + m_2} v\end{align*}$
where $v$ and $v'$ are the initial and final velocities of the particle initially not at rest. Plug in $m_1 = 4$ and $v' = -0.6v$ .
$\begin{align*}-0.6 v = \frac{4 u - m_2}{4 u + m_2} v\end{align*}$
Then solve for $m_2$ :
$\begin{align*}0.4 m_2 = 4 u + 2.4 u = 6.4 u \Rightarrow m_2 = \boxed{16 u}\end{align*}$
Therefore, answer (D) is correct.

Solution to 1996 Problem 20