1. The problem is to understand how to multiply integers. 2. When multiplying two integers, the sign of the product depends on the signs of the factors. 3. If both integers have the same sign (both positive or both negative), the product is positive. 4. If the integers have different signs (one positive, one negative), the product is negative. 5. For example, $3 \times 4 = 12$ (positive times positive is positive). 6. Another example, $-3 \times -4 = 12$ (negative times negative is positive). 7. And, $3 \times -4 = -12$ (positive times negative is negative). 8. Finally, multiplying by zero always gives zero, e.g., $5 \times 0 = 0$. This is the fundamental rule for multiplying integers.