Suppose y varies directly as the square of x and inversly as the cube of w. We know that y=9 when x=2 and w=1. Find y when x=4 and w=2.
The first sentence is telling you the following formula is correct (where k is the 'constant of variation'): $\displaystyle y=k\frac{x^2}{w^3}$
Use the information in the second sentence to solve for k. Once you know that, you can use the equation to get the answer to the third sentence.
$\displaystyle y \propto x^2$, so $\displaystyle y = k_1x^2$.
Substitute $\displaystyle x$ and $\displaystyle y$ to find $\displaystyle k_1$.
$\displaystyle y \propto \frac{1}{w^3}$, so $\displaystyle y = \frac{k_2}{w^3}$.
Substitute $\displaystyle w$ and $\displaystyle y$ to find $\displaystyle k_2$.
Then you should be able to finish the question.