I can't remember how to solve this problem, but I'm pretty sure the answer is 14.
Nevermind, I do remember how to solve this.
First let's cube \(x-\frac{1}{x}=2\)
\((x-\frac{1}{x})^3=2^3\)
\(x^3-3x+\frac{3}{x}-\frac{1}{x^3}=8\)
\(x^3-\frac{1}{x^3}=8+3(x-\frac{1}{x})\)
\(x^3-\frac{1}{x^3}=8+3(2)\)
\(x^3-\frac{1}{x^3}=\boxed{14}\)