imc

We label the vertices of the cube as different letters and numbers shown above. We label these so that Erin can only crawl from a number to a letter or a letter to a number (this can be seen as a coloring argument). The starting point is labeled $A$. If we define a "move" as each time Erin crawls along a single edge from one vertex to another, we see that after 7 moves, Erin must be on a numbered vertex. Since this numbered vertex cannot be one unit away from $A$ (since Erin cannot crawl back to $A$), this vertex must be $4$. Therefore, we now just need to count the number of paths from $A$ to $4$. To count this, we can work backwards. There are 3 choices for which vertex Erin was at before she moved to $4$, and 2 choices for which vertex Erin was at 2 moves before $4$. All of Erin's previous moves were forced, so the total number of legal paths from $A$ to $4$ is $3\cdot 2=\boxed{\text{6}}$.