Paths on a grid: number of routes problem

[bbl]

The problem is, how many routes can one take to get to point A to B without backtracking?

I know that I can solve this by assigning numbers to the intersections and that the intersections add up. However, I got stumped at certain parts because of the two rectangles. I might have also gotten some parts wrong. I also know that I can utilize combinatorics but I am not exactly sure how since there are rectangles.

Any help is appreciated. Thank you!

 

[Dr.Peterson]

The problem is, how many routes can one take to get to point A to B without backtracking?

I know that I can solve this by assigning numbers to the intersections and that the intersections add up. However, I got stumped at certain parts because of the two rectangles. I might have also gotten some parts wrong. I also know that I can utilize combinatorics but I am not exactly sure how since there are rectangles.

Any help is appreciated. Thank you!
View attachment 29425

Please explain the picture, perhaps by showing us the actual problem you are trying to solve, and then explaining your work in words. I can't quite tell what paths are allowed, or what the numbers refer to, though I can guess.