Answer
$0$
Work Step by Step
We use the unit circle values to simplify.
Since $\sin{\frac{\pi}{3}}=\frac{\sqrt3}{2}$ and $\tan{\frac{\pi}{6}}=\frac{\sqrt3}{3}$, then
$2 \ \sin \frac{\pi}{3} -3 \tan \frac{\pi}{6} = (2) (\frac{\sqrt 3}{2})- (3) (\frac{\sqrt3}{3}) \\=\sqrt 3 - \sqrt 3 \\=0$
