The task is to find the count of hamiltonian cycle in $Q_3$. So I know the answer is $6$, but i don't know why or how to get it.
My first attempt was simple: I start from edge $6$, and I have $3$ $(2,5,8)$, then I have another $2$ (so I will get $3\cdot 2=6)$. But this doesn't help, because by choosing the first two edges of the cycle, we don't get any perticular Hamilton Cycle. Any tips?