1. **State the problem:** Find the value of $-32 \equiv ? \pmod{12}$. 2. **Recall the definition:** For integers $a$ and $m > 0$, $a \equiv r \pmod{m}$ means $r$ is the remainder when $a$ is divided by $m$. 3. **Calculate the remainder:** Divide $-32$ by $12$. $$-32 \div 12 = -2.666...$$ The integer quotient is $-3$ (since we take the floor for negative division). 4. **Find the remainder:** $$r = -32 - (-3 \times 12) = -32 + 36 = 4$$ 5. **Interpretation:** The remainder is $4$, so $$-32 \equiv 4 \pmod{12}$$ 6. **Answer:** The correct choice is **a. 4**.