AT-OEMO-FED1 2002 Problem 2

Find the greatest real number $C$ such that, for all real numbers $x$ and $y \neq x$ with $xy = 2$ it holds that $$\frac{((x + y)^2 - 6)((x - y)^2 + 8)}{(x-y)^2}\geq C.$$ When does equality occur?