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To simplify the expression \( 2(3u - 2) + 3(4u + 2) \), we can distribute and combine like terms.

1. **Distribute** each term:
   - For \( 2(3u - 2) \): \( 2 \cdot 3u = 6u \) and \( 2 \cdot -2 = -4 \).
   - For \( 3(4u + 2) \): \( 3 \cdot 4u = 12u \) and \( 3 \cdot 2 = 6 \).

   This gives:
   \[
   6u - 4 + 12u + 6
   \]

2. **Combine like terms**:
   - Combine \( 6u \) and \( 12u \) to get \( 18u \).
   - Combine \( -4 \) and \( 6 \) to get \( 2 \).

   So, the simplified expression is:
   \[
   18u + 2
   \]

### Final Answer:
\[
18u + 2
\]

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you simplify expressions with multiple terms inside parentheses?
2. What are the steps to combine like terms?
3. Can you apply the distributive property to three terms inside parentheses?
4. How would you simplify if there were variables with different powers?
5. What changes if we have subtraction or division outside the parentheses?

**Tip:** Always remember to distribute each term to every term inside the parentheses before combining like terms.

Simplify the expression 2(3u - 2) + 3(4u + 2).

Learn how to simplify the algebraic expression 2(3u - 2) + 3(4u + 2) using the distributive property and combining like terms. This step-by-step solution is suitable for students in Grades 7-8.

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