Answer
$(0,-4)$
Work Step by Step
By definition: $x=r\cdot \cos(\theta)$, $y=r\cdot \sin(\theta)$.
Here $r=4 \text{ and } \theta=\frac{3\pi}{2}$.
Hence, after plugging these in:
$x=4\cdot \cos(\frac{3\pi}{2})=4\cdot0=0$
$y=4\cdot \sin(\frac{3\pi}{2})=4\cdot(-1)=-4$
The point has coordinates $(0,-4)$ in the rectangular coordinate system.