Eulerian and Hamiltonian Graphs · Hard problem

Three triangles share a single hub vertex $0$: triangle $0\text{-}1\text{-}2$, triangle $0\text{-}3\text{-}4$, and triangle $0\text{-}5\text{-}6$ (nine edges total, no edges between the triangles except through $0$). A closed route crosses every edge of this graph exactly once. Not counting the very last step back to $0$, how many times does the route pass through the hub vertex $0$?