Answer
$\det (2B)^{-1}(AB)^T=\frac{5}{16}$
Work Step by Step
Since $A$ and $B$ are $4 \times 4$ matrix
$\det ((2B)^{-1}(AB)^T)=\det ((2B)^{-1}\det (AB)^T)=\frac{1}{\det (2B)}.\det (AB)=\frac{1}{2^4\det(B)}.\det (A).\det (B)=\frac{1}{16.3}.5.3=\frac{5}{16}$
