8.0.

From the condition, we know that the axis of symmetry of the parabola $l: x=2$.
Thus, $m=2$.
Let $l_{A B}: y=k x+b$. Then
$$
\left\{\begin{array} { l } 
{ - 3 = - k + b , } \\
{ 2 = 4 k + b }
\end{array} \Rightarrow \left\{\begin{array}{l}
k=1, \\
b=-2,
\end{array}\right.\right.
$$

Thus, $l_{A B}: y=x-2$.
By symmetry, we know that when $P$ is the intersection point of line $A B$ and $l$, $P A+P C$ achieves its minimum value, at this time, $n=2-2=0$.
8. Let the graph of the parabola $y=a x^{2}+b x+c$ pass through the points $A(-1,-3) 、 B(4,2) 、 C(0,2)$. Let $P$ be a moving point on the axis of symmetry of the parabola. If $P A+P C$ takes the minimum value when the coordinates of point $P$ are $(m, n)$, then $n=$ $\qquad$