9. Given that the function $f(x)$ is defined on $\mathbf{R}$, and satisfies:
(1) $f(x)$ is an even function;
(2) For any $x \in \mathbf{R}$, $f(x+4) = f(x)$, and when $x \in [0,2]$, $f(x) = x + 2$.

Then the distance between the two closest points of intersection between the line $y=4$ and the graph of the function $f(x)$ is $\qquad$.
9.4.

Draw the graph of the function $f(x)$ (as shown in Figure 3).
From Figure 3, it is easy to see that the distance between the two closest intersection points of the line $y=4$ and the graph of the function $f(x)$ is 4.