Suppose that $f$ is some function satisfying

$\frac{x-2}{\sqrt[\phantom{2}]{x^{2}12}-4}f(x)\frac{|x^2-4|}{2x-x^2}$

for all $x$ in $(0,2).$ Evaluate $\underset{x{2}^{-}}{lim}f(x).$ Fully justify your answer.