If nP4 = 6x nP3 find n

I don't understand how to get to the answer, which is 9.

n! / (n-4!) = 6(n!/(n-3)!)

n! / (n-4)! = 6n! / (n-3)!

1/(n-4)! = 6/(n-3)!

(n-4)! = (n-3)!/6

(n-4)! = (n-3)(n-4)!/6 [as k! = k * (k-1)! ]

1 = (n-3)/6

n-3 = 6

n=9