https://web2.0calc.com/questions/how-many-9-step-paths-are-there-from-nbsp-nbsp-to-nbsp-nbsp-which-pass-through-nbsp
This problem is slightly different than the one from the link.
lol
just saw someone with the same question as mine.
How many 9-step paths are there from E to G?
Permutations of (hhhhhvvvv)(5+4)!5!4!=9!5!4!=5!6∗7∗8∗95!4!=6∗7∗8∗94!=6∗7∗8∗92∗3∗4=6∗7∗8∗92∗3∗4=302424=126
Second soultion: