If $$\left(x^{2} - \frac{1}{x^{2}} = 4\sqrt{6}\right)$$, x > 1, what is the value of $$\left(x^{3} - \frac{1}{x^{3}}\right)$$?

A

$$20\sqrt{2}$$

B

$$24\sqrt{2}$$

C

$$18\sqrt{2}$$

D

$$22\sqrt{2}$$