We use the velocity addition formula:

$\begin{align*}v_{AC} = \frac{v_{AB} + v_{BC}}{1 + v_{AB} v_{BC}/c^2}\end{align*}$
with $v_{AB} = 0.3 c$ and $v_{BC} = 0.6 c$ . This gives,

$\begin{align*}v_{AC} = \boxed{0.763 c}\end{align*}$
Therefore, answer (D) is correct.

Solution to 1996 Problem 37