Your gain calc sounds right. Since they are both inverting, the input voltage V turns into -V for the first stage, but then it inverts again so it's back to V.
Two inversion equals a non inversion
The first opamp is inverting and has a gain of -4 if its signal source has a very low resistance.
The second opamp is not inverting and has a gain of 2.
So the complete circuit has a gain of -8 (it inverts).