Density function of random variable $|X|$ Suppose $X$ is uniformly distributed over $(-1,1)$. Can someone explain to me what it means to find the density function of random variable $|X|$? Is it the same with the probability density function, which is $\frac{1}{2}$ on $(-1,1)$.

I am assuming that you did not make a typo, meaning
you are given that $|X|$ follows a $\text{unif}(-1,1)$. Then 
you are simply looking for a height $h$ that makes the the area over
$(-1,1)$ equal 1:
$$h\cdot(1-(-1)) = 1.$$
implies that $h = 1/2$.
If you meant "Suppose $X\sim \text{unif}(-1,1)$, find the density of
$|X|$", then that is a different problem. This is probably an exercise 
in using a many-to-one change of variable. 
If that is the case, then yes, let $Y = |X|$. Then
$$f_Y(y) = 1.$$
