What number must be added to both numerator and denominator of 3/8 so that the result is 2/3?

In order to get the result of 2/3 from 3/8, you would have to first convert 3/8 into 24th's, which would be 9/24. You would then have to add 5/24 to the 9/24 to get the equivalent of 2/3 (in 24th's, which is 16/24).