Answer
c. $64\,cis\,\frac{\pi}{2}$
Work Step by Step
Using de Moivre's theorem ($z^{n}=r^{n} cis \,n\theta$ where $z=r\, cis\,\theta$ and $n$ is an integer), we get
$(4\,cis\,\frac{\pi}{6})^{3}=(4)^{3}(cis\,3\cdot\frac{\pi}{6})=64\,cis\,\frac{\pi}{2}$.
The right option is c.