adding 2 to the numerator and denominator of 2/3, as suggested in the answer posted below, works for this particular question, but please be aware that the method may not always work for all questions of this type. this is because we cannot tell if the fraction was simplified after numerator and denominator were each decreased by 2.

working backwards, the fraction could have been ...
(2+2)/(3+2) = 4/5, or
(4+2)/(6+2) = 6/8, or
(6+2)/(9+2) = 8/11, etc

i believe a question like this is normally to exercise the student's ability to form equations and solve equations.

let the fraction be x/y
(x-2)/(y-2) = 2/3 gives 3x-2y = 2
(x+1)/(y+1) = 5/6 gives 6x-5y = -1

solving together as simultaneous equations, gives ...
x = 4 & y =5
so the required fraction is 4/5.

this method will work even the the fractions were simplified after numerator and denominator each decrease by 2 or increase by 1.

thank u for the explaination