Walks, Paths and Connectivity · Superchallenge problem

Let $G$ be three triangles sharing a single common vertex $0$: triangles on $\{0,1,2\}$, $\{0,3,4\}$, and $\{0,5,6\}$. Find the number of closed walks of length $6$ at vertex $0$, minus the number of closed walks of length $6$ at vertex $1$.