Since y varies directly as \(w^2\), we can write the equation as \(y = kw^2\), where k is the constant of variation.

We can find the value of k by using the given information that when y = 8, w = 2. Substituting these values into the equation, we get \(8 = k(2)^2\), which simplifies to \(k = 2\). Now that we know the value of k, we can use the equation to find y when w = 3.

Substituting these values into the equation, we get \(y = 2(3)^2\), which simplifies to \(y = 18\). Therefore, when w = 3, y = 18.