For any regular polygon, the area can be expressed in terms of its apothem [tex]a[/tex] and its perimeter [tex]p[/tex] like this:
[tex]A =\frac{ap}{2}[/tex]
For the problem the apothem [tex]a=4\sqrt{3}[/tex]
So we need to find the perimeter. A regular hexagon is built up by equilateral triangles, so the radius is equal to each side, therefore the perimeter is given by:
[tex]p=6r=6(8)=48[/tex]
Finally, if we substitute in the first equation:
[tex]A =\frac{4\sqrt{3}\times 48}{2}=166.27[/tex]
