10. The general solution of the equation $\cos \frac{x}{4}=\cos x$ is $\qquad$ , and in $(0,24 \pi)$ there are $\qquad$ distinct solutions.
Solve:
$\frac{x}{4}=2 k \pi \pm x \Rightarrow x=\frac{8}{3} k \pi$ or $\frac{8}{5} k \pi(k \in \mathbf{Z}) \Rightarrow$ the general solution of the equation $\cos \frac{x}{4}=\cos x$ is $\left\{x \left\lvert\, x=\frac{8}{3} k \pi\right.\right.$ or $\left.x=\frac{8}{5} k \pi, k \in \mathbf{Z}\right\}$. Within the interval $(0,24 \pi)$, there are $\frac{8 \pi}{3}, \frac{16 \pi}{3}, 8 \pi, \frac{32 \pi}{3}$, $\frac{40 \pi}{3}, 16 \pi, \frac{56 \pi}{3}, \frac{64 \pi}{3}, \frac{8 \pi}{5}, \frac{16 \pi}{5}, \frac{24 \pi}{5}, \frac{32 \pi}{5}, \frac{48 \pi}{5}, \frac{56 \pi}{5}, \frac{64 \pi}{5}, \frac{72 \pi}{5}, \frac{88 \pi}{5}, \frac{96 \pi}{5}, \frac{104 \pi}{5}$, $\frac{112 \pi}{5}$, a total of 20.