Answer
The value is $0$.
Work Step by Step
As we know:
$\sin \left( \frac{\pi }{3} \right)=\frac{\sqrt{3}}{2}$ And $\tan \left( \frac{\pi }{6} \right)=\frac{1}{\sqrt{3}}$
Therefore, on solving equation (1), we get,
$\begin{align}
& 2\sin \frac{\pi }{3}-3\tan \frac{\pi }{6}=2\left( \frac{\sqrt{3}}{2} \right)-3\left( \frac{1}{\sqrt{3}} \right) \\
& =\sqrt{3}-\frac{3}{\sqrt{3}} \\
& =\sqrt{3}-\sqrt{3} \\
& =0
\end{align}$
