Okay, I actually haven't solved the problem but I quickly noticed some things.

First, we can ignore all horizontal lines (we can't move sideways so thinking about moving left or right isn't exactly correct).

Second, due to ignoring the horizontal lines, we can limit our problem to a rhombus shape (forgive me I don't know how to create diagrams).

Now instead of thinking it as a rhombus shape imagine it as a square (or a 4x4 grid as shown)

Take one corner as the entrance and the opposite corner as the exit and now it's become an easier path problem.

Hope this makes sense.