\[\left( 4\sqrt{3} - 3\sqrt{2} \right)^{2} + \sqrt{54}\left( 8 - 7\sqrt{6} \right) =\]
\[= 16 \cdot 3 - 24\sqrt{6} + 9 \cdot 2 + 3 \cdot \sqrt{6} \cdot 8 - 3\sqrt{6} \cdot 7\sqrt{6} =\]
\[= 48 - 24\sqrt{6} + 18 + 24\sqrt{6} - 126 =\]
\[= - 78.\]