Answer
$\dfrac{\sqrt3}{2}$
Work Step by Step
Substitute $\frac{\pi}{6}$ to $x$ to obtain:
$\sin{(2x)}= \sin{2(\frac{\pi}{6})}=\sin{(\frac{\pi}{3})}$
$\dfrac{\pi}{3}$ is a special angle whose sine value is $\dfrac{\sqrt{3}}{2}$.
Thus, when $x=\frac{\pi}{6}$,
$\sin{(2x)} = \dfrac{\sqrt3}{2}$
