\[4\sqrt{2} - 3\sqrt{8} + 2\sqrt{32} =\]
\[= 4\sqrt{2} - 3 \cdot 2\sqrt{2} + 2 \cdot 4\sqrt{2} =\]
\[= 4\sqrt{2} - 6\sqrt{2} + 8\sqrt{2} = 6\sqrt{2};\]
\[\left( 6\sqrt{2} \right)^{2} = 36 \cdot 2 = 72.\]
\[Ответ:72.\]