[![enter image description here](https://i.stack.imgur.com/DDKdl.png)](https://i.stack.imgur.com/DDKdl.png)

I am trying to figure out the symmetry factor of the above diagram in the $\phi^4$ theory. The correct answer is $S=4$ (in that the Feynman diagram gets a multiplicative factor of $\frac{1}{4}$) but I get $S=8$ with the following reasoning.

For each closed loop, we can exchange the lines that start/end in the loop and belong to it. So, each loop gives a factor of $2$. Moreover, we can exchange the two vertices and simultaneously exchange the propagators of each loop. This gives an extra factor of $2$. I think it's the last bit that I'm getting wrong. Peskin and Schroeder write (p.93) that "A third possible type of symmetry is the equivalence of two vertices" but I don't think I understand precisely what this statement means. For example, why would the two vertices of this particular Feynman diagram not be equivalent? We can simply rename the integration variables and interchange them.