[tex]\displaystyle{ \frac{1}{2} \cdot \sqrt{3} \cdot (-4\sqrt{3}) = \frac{\sqrt{3}}{2} \cdot (-4\sqrt{3}) }[/tex]
[tex]\displaystyle{ =\frac{-4\sqrt{3}\cdot \sqrt{3}}{2} }[/tex]
[tex]\displaystyle{ =-2 \cdot 3 }[/tex]
[tex]\boxed{=-6}[/tex]
