Eulerian and Hamiltonian Graphs · Medium problem

Two copies of $K_4$ share exactly one edge: one $K_4$ on $\{1,2,3,4\}$, another on $\{1,2,5,6\}$, with edge $12$ common to both ($6$ vertices total, $11$ distinct edges). Counting a cycle and its reverse as the same, how many Hamiltonian cycles does this graph have?