We can make a drawing to see better:
In the picture above, we can see the sides AC and BC are equals because triangle ABC is isosceles, and also the segments AD and DB are equals for the same reason.
We can calculate the lenght of segment AD as:
[tex]\begin{gathered} \tan (30)=\frac{CD}{AD} \\ AD=\frac{CD}{\tan (30)}=\frac{4}{\frac{1}{\sqrt[]{3}}} \\ AD=4\cdot\sqrt[]{3} \end{gathered}[/tex]
With the lenght of segment AD we can calculate the lenght of AB as:
[tex]AB=2\cdot AD=8\cdot\sqrt[]{3}[/tex]
The correct answer is in yellow.
