I haven't seen anything like it before, so I'm getting something far off, I might just be very very wrong.

But I can't figure out where.

For each vertex, there are $4$ choices for picking $a$'s transitions, $4$ choices for picking $b$'s transitions, and there are $4$ such vertices.

And all states should be non-final in order reject every possible string in the language including $\epsilon$.

So, my answer gives $4^3 = 64$