Let $X$ and $Y$ be two independent random variables.
Let $Z=g(X,Y)$ a function of two random variables. To find the CDF of $Z$ we have
\begin{align} P\{Z\leq z\}=&P\{g(X,Y)\leq z\}\\ =&\iint_{g(x,y)\leq z}^{}f_X(x)f_Y(y) dxdy. \end{align}
In Books, The inequality $g(x, y) ≤ z$ defines a region in the $(x, y)$ plane. How we find this region? For exaple $Z=X+Y$.