Math Counting Question - How many possible routes

There are 3 routes from City A to City B.
There are 5 routes from City B to City C.
Without traveling on the same route twice, how many different ways are there to get from
City A to City B to City C, back to City B, to City A?

You can get to B 3 different ways. From there, you can take 5 different paths to C.
3*5 = 15
Now, you cannot travel on the original route you went on, so you eventually have to subtract by 1.
15*2 = 30 (you have to go back)
30-1 = 29 (you have to eliminate the original route you took)
Your answer should be 29.