Unsure of what you mean by "6-23." There's no subtraction in this problem.
If you meant "6/23," then "doubling" that results in 12/23 cups. Still, that does not look right. Go back and ensure that you have copied down the original problem exactly.
The equation out of this is; what is 250/100 of a number x = 90? => Division of 250 by 100 gives 2.5. => Now multiply 2.5 by a number x resulting to 2.5x on the L.H.S. => make x the subject and come up with x = 90/2.5. answer is 1/36.