A cat walk
Today Hakase will be taking Sakamoto-san for a walk (that's a cat). Unfortunately, they ended in town district that is notorious for dogs.
The district has 18 streets, 9 vertical, 9 horizontal (image above). If intersections marked with the triangle are "dog spots" (places where a person will definetely encounter a dog ), on how many ways Hakase and Sakamoto-san can arive safely to the finish point.
Hints: Assume that they will only go up and right.