2. \(4\sqrt{6}-\sqrt{54}+\sqrt{24}\cdot\sqrt{6}\)

Упростим корни: \(\sqrt{54}=3\sqrt{6}\), \(\sqrt{24}=2\sqrt{6}\).

\(4\sqrt{6}-3\sqrt{6}+2\sqrt{6}\cdot\sqrt{6}=\sqrt{6}+12\).

Ответ: \(12+\sqrt{6}\).