MHB Q&A: Understanding Part C of a Round Trip Problem

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The discussion centers on the confusion regarding the calculation of return routes in part c of a round trip problem. The answer key indicates there are 14 ways to reach point C, but the user believes the return options vary based on the road taken. They argue that if certain roads are used to reach C, it limits the return routes differently depending on which roads are restricted. The user concludes that if R1R5 is used to get to C, the only restricted return trip is R5R1, allowing for other routes back. The core issue is the misunderstanding of how the restrictions on return trips affect the total number of valid routes.
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I don't understand the answer for part c of the following question

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The answer key gives 14x13 as the solution to part c. I understand there are 14 ways to get to point C but depending on which road can no longer be used, there is anywhere between 10 and 13 ways to return home. For example, say R8 was taken to get to C. Then there are 14-1 ways to make the return trip (just don't use R8). However, if R1R5 is used then we can't use either R1 (so now there are 3x3+2=11 ways to make the trip) or R5 (so now there are 2x4+2=10 ways to make the trip). What is wrong with my reasoning?
 

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As I understand the problem statement in c), if Linda takes R1R5 to get from A to C, there is a single trip she is not allowed to take back: R5R1. All other trips are allowed.
 

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