So the problem is to find $\displaystyle P(|Z|\in [3/2, 5/2])$? That has nothing to do with y.
Z is the uniform distribution from -2 to 2 so have value Z(z)= 1/4 for all z for all z between -2 and 2. $\displaystyle |Z|\in [3/2, 5/3]$ is the same as $\displaystyle Z\in [-2, -3/2]\cup [3/2, 2]$. Those two intervals are disjoint so that is $\displaystyle P(Z\in [-2, -3/2]+ P(Z\in [3/2, 2])$. And each of those is just 1/4 times the length of the interval.
There is a tutorial on "Latex" at Beginning LaTeX.
On this board start each latex code with [ tex ] and end with [ /tex ] (without the spaces)- or just press the $\displaystyle \Sigma$ key in the menu above.