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 intersection points of the line $y=4$ and the graph of the function $f(x)$ is $\qquad$