Let's simplify the expression step by step:

Given:  
\[ 3p + 4(p - 2) - 2(s + 6) - 2s - 2p \]

1. **Distribute the multiplication** for the terms inside the parentheses:
   \[
   3p + 4p - 8 - 2s - 12 - 2s - 2p
   \]

2. **Combine like terms** for \(p\) and \(s\), and the constants:
   - For \(p\): \(3p + 4p - 2p = 5p\)
   - For \(s\): \(-2s - 2s = -4s\)
   - For the constants: \(-8 - 12 = -20\)

   So, the expression simplifies to:
   \[
   5p - 4s - 20
   \]

Thus, the simplified expression is:

\[
\boxed{5p - 4s - 20}
\]

Would you like to know more details, or do you have any questions about the steps?

Here are 5 related questions to expand on this topic:
1. How do you solve linear equations involving multiple variables?
2. What are the common rules for distributing multiplication over addition or subtraction?
3. How can you factor expressions like \(5p - 4s - 20\)?
4. What is the significance of combining like terms in algebra?
5. How do you handle more complex expressions with multiple distribution steps?

**Tip:** Always perform operations step-by-step to avoid mistakes, especially when distributing and combining like terms.

Learn how to simplify the expression 3p + 4(p - 2) - 2(s + 6) - 2s - 2p with a step-by-step solution. This problem involves algebraic manipulation using the distributive property and combining like terms. Suitable for students in Grades 7-9.

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