Let A be a square matrix of order 3 such that det (A)=-2 and det (3 adj (-6 adj (3 A )))=2^m + n · 3^mn, m > n. Then 4 m +2 n is equal to ____.

Let $\displaystyle A$ be a square matrix of order $\displaystyle 3$ such that $\displaystyle \operatorname{det}(A)=-2$ and $\displaystyle \operatorname{det}(3 \operatorname{adj}(-6 \operatorname{adj}(3 \mathrm{~A})))=2^{\mathrm{m}+\mathrm{n}} \cdot 3^{\mathrm{mn}}, \mathrm{m}>\mathrm{n}$. Then $\displaystyle 4 \mathrm{~m}+2 \mathrm{n}$ is equal to $\displaystyle \_\_\_\_$.