Answer
$(\frac{\sqrt 6}{2},\frac{\sqrt 6}{2},1)$.
Work Step by Step
Since $\rho=2, \, \theta=\frac{\pi}{4}, \, \phi=\frac{\pi}{3}$ and
$$ x=\rho\cos \theta\sin \phi,\quad y=\rho\sin\theta\sin\phi, \quad z=\rho\cos \phi,$$
then we have
$$ x=2\cos \frac{\pi}{4}\sin \frac{\pi}{3}=\frac{\sqrt 6}{2}, $$
$$ y=3\sin \frac{\pi}{4}\sin \frac{\pi}{3}=\frac{\sqrt 6}{2}, $$
$$ z=3\cos \frac{\pi}{3}=1.$$
Hence, the rectangular coordinates are $(\frac{\sqrt 6}{2},\frac{\sqrt 6}{2},1)$.
