\[\left( 2\sqrt{3} - 3\sqrt{2} \right)^{2} + 12\sqrt{6} =\]
\[= 4 \cdot 3 - 12\sqrt{3 \cdot 2} + 9 \cdot 2 + 12\sqrt{6} =\]
\[= 12 + 18 - 12\sqrt{6} + 12\sqrt{6} = 30.\]