Which of the following is equivalent to -x/3 ≤ 4?

Start with $-\frac{x}{3} \leq 4$. Multiply both sides by $-3$. Multiplying by a negative number reverses the inequality, so $x \geq -12$, choice C. Check with $x = 0$: $0 \leq 4$ is true, and $0 \geq -12$ is true. Choice A ($x \leq -12$) has the right number but keeps the original direction of the inequality. Choice B ($x \geq 12$) flips the sign but loses the negative sign on the number. Choice D ($x \leq 12$) both loses the sign and keeps the original direction. Test a point such as $x = 20$: $-\frac{20}{3} \leq 4$ is true, so large values belong, consistent with C.