Find $Y = |X|$ for a PDF of X (Solution Check) I am given a PDF:
$$
f_X(x) = \frac{\ell}{2}e^{-\ell |x|}
$$
with boundaries
$-\infty < x < \infty$ and $\ell > 0$.
I am asked to find $f_Y(y)$ if $Y = |X|$.

My try is:
\begin{align}
F_Y(y) &= P(Y \leq y)\\ &= P(-y \leq X \leq y)\\ &= F_X(y) - F_X(-y)
\end{align}
Now I take the derivative of that, to find
\begin{align}
f_Y(y) &= f_X(y)\frac{dy}{dy} - f_X(-y)\frac{d(-y)}{dy}\\ &= f_X(y) + f_X(-y)\\ &= \frac{\ell}{2}e^{-\ell y} + \frac{\ell}{2}e^{-\ell y}\\ &= \ell e^{-\ell y}
\end{align}
Is what I am doing correct?

Yes, that is correct.  Also note that in the course of your calculations you effectively derived  the general rule (for a continuous random variable):
$$f_{|X|}(x) = f_X(x) + f_X(-x).$$
