I'm stuck on part c) of this question. The answer key gives 182. I already know there are 14 ways to make the trip from city A and city B and vice versa. It appears 182 came from $14 \times 13$ but I don't get where 13 came from? If neither $R_8$ or $R_9$ were used on the trip there, one of the roads in the middle would need to be removed from the return trip so that would become $2 \times 4$ or $3 \times 3$.
By the way, what's the policy for this site regarding typing out questions instead of putting images for them? Normally I would try but if a person can't view images then they wouldn't be able to see the graph and wouldn't be able to help anyways.