Let $G$ be a simple planar graph with fewer than 12 faces. Suppose that each vertex of $G$ has degree at least $3$. prove that $G$ and its dual are 4-colorable.
I'm not too sure how to approach this one and I really need to get better with proofs. But anyway, I know from a previous exercise that the faces of $G$ cannot be bounded by more than 4 edges. More specifically, $m \leq 3f - 6$ where $m$ is the number of edges and $f$ is the number of faces in the graph $G$. However, I'm not sure where to go from here. Any help would be appreciated.