-31 + 31 + 4 (mod 9) 12 - 14 (mod 6) 99 (mod 5) - 34 (mod 5) 12 x 12 (mod 5)

Since $4 < 9$, the remainder is 4.

$$-31 + 31 + 4 \equiv 4 \pmod 9$$

The final answer is $\boxed{\text{4}}$.

3. $12 - 14 \pmod 6$

To get a positive remainder, add the modulus until the number is non-negative.

$$-2 + 6 = 4$$ $$12 - 14 \equiv 4 \pmod 6$$

The final answer is $\boxed{\text{4}}$.

4. $99 \pmod 5 - 34 \pmod 5$

$$99 = 19 \times 5 + 4$$

So, $99 \equiv 4 \pmod 5$.

$$34 = 6 \times 5 + 4$$

So, $34 \equiv 4 \pmod 5$.

$$99 \pmod 5 - 34 \pmod 5 \equiv 4 - 4 \pmod 5$$ $$4 - 4 = 0$$

$$0 \equiv 0 \pmod 5$$

The final answer is $\boxed{\text{0}}$.

5. $12 \times 12 \pmod 5$

$$12 = 2 \times 5 + 2$$

So, $12 \equiv 2 \pmod 5$.

$$12 \times 12 \pmod 5 \equiv 2 \times 2 \pmod 5$$ $$2 \times 2 = 4$$

Since $4 < 5$, the remainder is 4.

$$12 \times 12 \equiv 4 \pmod 5$$

The final answer is $\boxed{\text{4}}$.