6. Use 4 different colors to paint the faces of a regular tetrahedron, with each face painted one color, and no face left unpainted. There are () different ways to do this.
(A) 48
(B) 36
(C) 42
(D) 47
6. B.

Using one color has $\mathrm{C}_{4}^{1}=4$ different ways of coloring; using two colors has $\mathrm{C}_{4}^{2} \times 3=18$ different ways of coloring; using three colors has $\mathrm{C}_{4}^{3} \cdot \mathrm{C}_{3}^{1}$ $=12$ different ways of coloring; using four colors has $\mathrm{C}_{4}^{4} \cdot \mathrm{C}_{2}^{1}=2$ different ways of coloring. In total, there are $4+18+12+2=36$ ways.