What I mean is the following:
$\displaystyle 2x^2=3y^3$
$\displaystyle \Leftrightarrow y=\sqrt[3]{\frac{2x^2}{3}}$ (1)
Because the question asks how y increases if x is multiplied by two you have to replace x by 2x
$\displaystyle \Leftrightarrow y=\sqrt[3]{\frac{2(2x)^2}{3}}$
$\displaystyle \Leftrightarrow y=\sqrt[3]{\frac{2\cdot 4x^2}{3}}$
$\displaystyle \Leftrightarrow y=\sqrt[3]{4}\cdot \sqrt[3]{\frac{2x^2}{3}}$ (2)
So you recognize an equal part in (1) and (2), but (2) is multiplied by a factor ... ?
If you understand how Siron got that answer then use your laws of exponents to say that $\displaystyle \sqrt[3]{4} = 4^{1/3}$
Edit: The question is asking to find the difference in "scale" if you will. In other words it wants you to find $\displaystyle \dfrac{f(2x)}{f(x)}$ where f(x) is the equation given.
From Siron's post the answer is eq2/eq1