As I read it, your original numerator is 8x-2y3 and
the original denominator is 4x½y-2.
8/4 gives coefficient 2
Placing x squared in denominator to rid yourself of the negative exponent, and placing y squared in numerator for the same reason, you now will have
To RATIONALIZE DENOMINATOR, multiply both top & bottom by an additional x½ and you then get the correct answer.