It's like any other problem - practice in algebraic manipulation, symbolic representation, and careful attention to the problem statement.
In this case, there is only one equation, so it is unlikely that you can find specific values for both x and y. For this reason, they ask for the ratio x:y.
Finally, before you get started, you have written \(\displaystyle \dfrac{7}{2x} - 3y = \dfrac{8}{4x} - 6y\). Is this your intent? If not , use parentheses or LaTeX to clarify meaning.