The cdf is $F(y) = \Pr(-2 \ln X < y) = \Pr \left( \ln X > - \frac{y}{2} \right) = \Pr \left(X > e^{-y/2} \right) = 1 - \Pr \left(X < e^{-y/2} \right)$ for $0 < y < +\infty$ and zero otherwise.