There are 5 different routes that a commuter can take from her home to the office. in how many ways can she make a round trip if she uses a different route coming than going?

Well to find this we need to multiply the amount of different routes that she can take TO work by the number of options that she can then take home FROM work that are different to the one that she took to work.
This means that the answer is 5*4 = 20 different ways