1. The problem asks to find which equation has a constant of proportionality equal to 4. 2. The constant of proportionality $k$ in an equation of the form $y = kx$ relates $y$ and $x$ directly. 3. We need to rewrite each equation in the form $y = kx$ to identify $k$. 4. For option A: $4y = 4x$. Divide both sides by 4: $$\cancel{4}y = \cancel{4}x \implies y = x$$ So, $k = 1$. 5. For option B: $4y = 12x$. Divide both sides by 4: $$\cancel{4}y = \frac{12}{\cancel{4}}x \implies y = 3x$$ So, $k = 3$. 6. For option C: $3y = 4x$. Divide both sides by 3: $$\cancel{3}y = \frac{4}{\cancel{3}}x \implies y = \frac{4}{3}x$$ So, $k = \frac{4}{3}$. 7. For option D: $3y = 12x$. Divide both sides by 3: $$\cancel{3}y = \frac{12}{\cancel{3}}x \implies y = 4x$$ So, $k = 4$. 8. The constant of proportionality equal to 4 is found in option D. Final answer: Option D has the constant of proportionality equal to 4.