\[\sqrt{24} - 4\sqrt{6} + \sqrt{54} =\]
\[= \sqrt{4} \cdot \sqrt{6} - 4\sqrt{6} + \sqrt{9} \cdot \sqrt{6} =\]
\[= 2\sqrt{6} - 4\sqrt{6} + 3\sqrt{6} = \sqrt{6}\]