Let $A$ and $B$ be two square matrices of order $3$ such that $|A| = 3$ and $|B| = 2$. Then $\left| A^{T} A \,(\text{adj}(2A))\,(\text{adj}(4B))\,(\text{adj}(AB))^{-1} A A^{T} \right|$ is equal to: