Let's go through the problems step-by-step, applying the distributive property where needed. I’ll solve each question one by one:

1) $2(a + 3) = -12$

• Distribute the 2: $2 \cdot a + 2 \cdot 3 = -12$
• Simplify: $2a + 6 = -12$
• Subtract 6 from both sides: $2a = -18$
• Divide by 2: $a = -9$

2) $3(p + 2) = 18$

• Distribute the 3: $3 \cdot p + 3 \cdot 2 = 18$
• Simplify: $3p + 6 = 18$
• Subtract 6 from both sides: $3p = 12$
• Divide by 3: $p = 4$

3) $4(2 + s) = 88$

• Distribute the 4: $4 \cdot 2 + 4 \cdot s = 88$
• Simplify: $8 + 4s = 88$
• Subtract 8 from both sides: $4s = 80$
• Divide by 4: $s = 20$

4) $2(3a + 2) = -8$

• Distribute the 2: $2 \cdot 3a + 2 \cdot 2 = -8$
• Simplify: $6a + 4 = -8$
• Subtract 4 from both sides: $6a = -12$
• Divide by 6: $a = -2$

5) $4 = 4(k + 3)$

• Distribute the 4: $4 = 4k + 12$
• Subtract 12 from both sides: $-8 = 4k$
• Divide by 4: $k = -2$

6) $5 = 5(y - 2)$

• Distribute the 5: $5 = 5y - 10$
• Add 10 to both sides: $15 = 5y$
• Divide by 5: $y = 3$

7) $- (3k - 12) = 48$

• Distribute the negative sign: $-3k + 12 = 48$
• Subtract 12 from both sides: $-3k = 36$
• Divide by -3: $k = -12$

8) $-2(x - 3) = 18$

• Distribute the -2: $-2x + 6 = 18$
• Subtract 6 from both sides: $-2x = 12$
• Divide by -2: $x = -6$

Let me know if you would like further details on any of these solutions or if you have any other questions.

Here are some related questions to expand your understanding:

1. How would these solutions change if the signs were reversed in each equation?
2. Can you solve similar equations with different coefficients using the same steps?
3. What happens if you apply the distributive property incorrectly? How does it affect the answer?
4. How do you check if your solution is correct for each equation?
5. Why is it important to isolate the variable on one side of the equation?

Tip: Always remember to distribute multiplication across addition or subtraction carefully to avoid mistakes.