1. The problem states that $y$ varies directly as $x$, which means the relationship can be written as $y = kx$ where $k$ is a constant. 2. We are given that $y = 21$ when $x = 6$. Substitute these values into the equation to find $k$: $$21 = k \times 6$$ 3. Solve for $k$: $$k = \frac{21}{6}$$ 4. Simplify the fraction: $$k = \frac{\cancel{21}}{\cancel{6}} = \frac{7}{2}$$ 5. Now, use the value of $k$ to find $y$ when $x = 14$: $$y = \frac{7}{2} \times 14$$ 6. Multiply: $$y = 7 \times \cancel{\frac{14}{2}} = 7 \times 7 = 49$$ **Final answer:** $y = 49$ when $x = 14$.