4. The faces of a regular hexahedron and a regular octahedron are all equilateral triangles with side length $a$. The ratio of the radii of the inscribed spheres of these two polyhedra is a simplest fraction $\frac{m}{n}$. Then, the product $m n$ is ( ).
(A) 3
(B) 4
(C) 6
(D) 12
4. C.

Using the equal volume method, we can find that $\frac{m}{n}=\frac{2}{3}$. Therefore, $m n=6$.