Answer
$4$
Work Step by Step
To find the Jacobian, we calculate the determinant of the 2x2 matrix $\frac{\partial(x, y)}{\partial(r, \theta)}$ as follows $$
\operatorname{Jac}(G)=\frac{\partial(x, y)}{\partial(r,\theta)}=\left|\begin{array}{ll}
{\frac{\partial x}{\partial r}} & {\frac{\partial x}{\partial \theta}} \\
{\frac{\partial y}{\partial r}} & {\frac{\partial y}{\partial\theta}}
\end{array}\right|=\left|\begin{array}{ll}
{ \cos \theta} & {-r\sin\theta} \\
{\sin\theta} & {r\cos\theta}
\end{array}\right| =r\cos^2 \theta+r\sin^2\theta=r.
$$
Now, at the point $(r,\theta)= (4,\pi/6)$, we have $
\operatorname{Jac}(G)=4.$
