The method of moments estimator sets the sample mean equal to the population mean.
So, in a way you have two n's.
By the way, that data doesn't look like it would come from a Bin(250,p).
But what you should do is compute the sample mean of 1 through 8
which is (8)(9)/2=45 divided by 8 or 4.5 and set that equal to 250p and solve for p.
This data is hardly from a bin(250,p) distribution.
Maybe more of a Poisson.