Simplify the given expression.

$(x -\frac{2}{x})^3 - ( x + \frac{2}{x})^3$

$-4(3x +\frac{4}{x^3})$

$(x -\frac{2}{x})^3 - ( x + \frac{2}{x})^3$

Put the value of x  = 1 and satisfy from the options ,

$(x -\frac{2}{x})^3 - ( x + \frac{2}{x})^3$ = $(1 -\frac{2}{1})^3 - (1 + \frac{2}{1})^3$ = -28

Now check from the options , and if we choose $-4(3x +\frac{4}{x^3})$

$-4(3x +\frac{4}{x^3})$ = $-4(3(1) +\frac{4}{1^3})$ = -28 (Satisfied)

So the value of $(x -\frac{2}{x})^3 - ( x + \frac{2}{x})^3$ = $-4(3x +\frac{4}{x^3})$