if m and n are positive integers, and if m is 250% of n, what percent of m is 2n?

m is 250% of n means that m is bigger than n, and by 2.5 times.

So, the equation you would use would be:
m = 2.5n

Because you need to multiply n by 2.5 to make it as big as m.

Now, if n was twice as large as it already is, what would be the percentage?

For example, those numbers:

5 (m), 2 (n)

m is 2.5 times as big as n.

To make them equal, you multiply n by 2.5:
5 = 2.5(2)
5 = 5

Which is true.

Now, imagine if n was twice as big, 2*2 = 4.

You are being asked what value (say, "v") you should put here:
5 = v*4