1. The problem states that two quantities, $x$ and $y$, are directly proportional. This means we can write the relationship as: $$y = kx$$ where $k$ is the constant of proportionality. 2. We are given that $y = 16$ when $x = 12$. Substitute these values to find $k$: $$16 = k \times 12$$ 3. Solve for $k$: $$k = \frac{16}{12} = \frac{\cancel{16}}{\cancel{12}} \times \frac{4}{3} = \frac{4}{3}$$ 4. Now, find $y$ when $x = 9$ using the formula $y = kx$: $$y = \frac{4}{3} \times 9$$ 5. Simplify: $$y = \frac{4}{3} \times 9 = 4 \times \cancel{3} = 12$$ **Final answer:** $y = 12$ when $x = 9$.