Answer
$\dfrac{\sqrt3}{4}$
Work Step by Step
RECALL:
$(f\cdot g)(x)=f(x)\cdot g(x)$
Use the rule above to obtain:
$(f\cdot g)\left(\dfrac{4\pi}{3}\right)=\sin{\left(\dfrac{4\pi}{3}\right)} \cdot \cos{\left(\dfrac{4\pi}{3}\right)}=-\dfrac{\sqrt3}{2} \cdot \left(-\dfrac{1}{2}\right)=\dfrac{\sqrt3}{4}$
