Answer
$x=\dfrac{2\pi}{3}$
Work Step by Step
Divide $2\sqrt3$ to both sides of the equation:
$\dfrac{2\sqrt3\sin{(\frac{x}{2})}}{2\sqrt3}=\dfrac{3}{2\sqrt3}
\\\sin{(\frac{x}{2})}=\dfrac{\sqrt3}{2}$
RECALL:
$\sin{x}=a \longrightarrow x=\sin^{-1}{(a)}$
Use the definition above to obtain:
$\dfrac{\pi}{2}=\sin^{-1}{(\frac{\sqrt3}{2})}$
Use the inverse sine function of a calculator to obtain:
\begin{array}{ccc}
&\frac{x}{2} &= &\frac{\pi}{3}
\\&2\cdot \frac{x}{2} &= &\frac{\pi}{3} \cdot 2
\\&x &= &\frac{2\pi}{3}
\end{array}
