2. The general solution of the equation $\cos \frac{x}{4}=\cos x$ is ( ), and in the interval $(0,24 \pi)$, there are ( ) distinct solutions.
2. The original equation $\cos \frac{x}{4}=\cos x$ can be transformed into
$$
\cos x-\cos \frac{x}{4}=0
$$

which is
$$
-2 \sin \frac{5 x}{8} \sin \frac{3 x}{8}=0 \text {. }
$$

From $\sin \frac{5 x}{8}=0$, we get $\frac{5 x}{8}=m \pi, x=\frac{8 m \pi}{5} \quad(m \in \mathbb{Z})$
From $\sin \frac{3 x}{8}=0$, we get $\frac{3 x}{8}=n \pi, x=\frac{8 n \pi}{3} \quad(n \in \mathbb{Z})$
Notice that the function $f(x)=\cos x-\cos \frac{x}{4}$ is a periodic function with a period of $8 \pi$, and within one period $(0,8 \pi)$, the roots of $f(x)=0$ are
$$
0, \frac{8 \pi}{5}, \frac{16 \pi}{5}, \frac{24 \pi}{5}, \frac{32 \pi}{5} \text { and } \frac{8 \pi}{3}, \frac{16 \pi}{3}
$$

There are 7 in total. Therefore, the number of distinct solutions in $(0,24 \pi)$ is
$$
3 \times 7-1=20 \text { solutions. }
$$

Answer: The general solution to $\cos \frac{x}{4}=\cos x$ is
$$
x=\frac{8 m}{5} \pi \text { or } x=\frac{8 n \pi}{3},
$$

where $m, n \in \mathbb{Z}$. In $(0,24 \pi)$, there are 20 distinct solutions.