TITLE: Number of paths in a board with a puncture
QUESTION [6 upvotes]: A picture of the board and my solution

I have this $8 \times 6$ board but there is a restriction with it - we have a hole with a bottom-left corner at $(3, 2)$ and top-right at $(6, 4)$. I need to count the number of possible ways to get from the top-left corner to the bottom-right corner of the board.
Since there are two ways to go around the hole, I counted them and summed them. Is my solution correct or did I miss something?
Thank you in advance!

REPLY [3 votes]: Here is a variant which evaluates  the number of valid lattice paths by iteratively adding up the number of valid paths with  shorter length.
                   
We conclude  in concordance with the  answer of @ParclyTaxel:
The number of valid paths is $$\color{blue}{1358}$$