1. The problem is to multiply $-6$ by $7$. 2. The multiplication rule for integers states that when multiplying a negative number by a positive number, the result is negative. 3. Multiply the absolute values: $$6 \times 7 = 42$$ 4. Apply the sign rule: since one number is negative and the other positive, the product is negative. 5. Therefore, $$-6 \times 7 = -42$$ 6. The final answer is $-42$.