Let $G$ be a 3-regular connected planar graph with a planar embedding where each face has degree either 4 or 6 and each vertex is incident with exactly one face of degree 4. Determine the number of vertices, edges and faces of degree 4 and 6.
Using handshake lemmas and Euler Formula, I've come up with the following for $E$ edges and $n$ vertices:
I'm missing an equation because I'm not sure how to use the restriction where each vertex is incident with one face of degree 4. Any help?