How can we verify whether the shortest route is really the shortest?

Question

I found the following question:

I had fun solving the problem and got the following answer (which is correct according to the book):

However, if I wasn’t able to check the answer in the back of the book, how can I be sure that this is the shortest route?

Answer 1

You can try opening up the cube. For example, if you rotate the back face by $90º$ so that it is parallel to the left face, then the line you drew becomes a straight line.

This proves that your solution is the shortest solution.