Correct Answer: $0$

Solution : Given: $2\sqrt{54} - 6\sqrt{\frac{2}{3}} - \sqrt{96}$
By simplifying this expression, we get:
= $2\sqrt{2\times3\times3\times 3} - (2\times3)\sqrt{\frac{2}{3}} - \sqrt{2\times 2\times 2\times 2\times 2\times 3}$
= $6\sqrt{6} - 2\sqrt{\frac{2}{3}\times9} - 4\sqrt{6}$
= $6\sqrt{6} -  2\sqrt{6} - 4\sqrt{6}$
= $6\sqrt{6} - 6\sqrt{6}$
= $0$
Hence, the correct answer is $0$.