4. As shown in Figure 2, given the slant height of the cone $O A=6$, and the radius of the base circle is 2. A small insect starts at point $A$ on the base of the cone, travels around the lateral surface of the cone, and returns to point $A$. The shortest distance the insect travels is ( ).
(A) 12
(B) $4 \pi$
(C) $6 \sqrt{2}$
(D) $6 \sqrt{3}$
4.D.

Draw the lateral development (as shown in Figure 7). Connect $A A^{\prime}$, then $A A^{\prime}$ is the shortest distance. Let $\angle A O A^{\prime}=n^{\circ}$. Since $\overparen{A A^{\prime}}=4 \pi$, then $4 \pi=\frac{6 n \pi}{180}$, so $n=120$. Therefore, $A A^{\prime}=6 \sqrt{3}$.