$ =\left.\left|3.2^2\right| \mathrm{A}\right|^4 \operatorname{adj}\left(\left.\operatorname{adj}(\mathrm{A})\left|=2^6 3^3\right| \mathrm{A}\right|^{12}|\mathrm{~A}|^4\right. $

$ =2^6 3^3|\mathrm{~A}|^{16}=2^{-10} 3^{-13} $

$ \Rightarrow|\mathrm{A}|^{16}=2^{-16} 3^{-16} \Rightarrow|\mathrm{A}|=2^{-1} 3^{-1}$

$ \text { Now }|3 \operatorname{adj}(2 \mathrm{~A})|=\left|3.2^2 \operatorname{adj}(\mathrm{A})\right| $

$ =2^6 3^3|\mathrm{~A}|^2=2^{-\mathrm{m}} 3^{-\mathrm{n}} $

$ \Rightarrow 2^6 3^3 2^{-2} 3^{-2}=2^{-\mathrm{m}} 3^{-\mathrm{n}} $

$ \Rightarrow 2^{-\mathrm{m}} 3^{-\mathrm{n}}=2^4 3^1 $

$ \Rightarrow \mathrm{m}=-4, \mathrm{n}=-1 $

$ \Rightarrow|3 \mathrm{~m}+2 \mathrm{n}|=|-12-2|=14$