Let's simplify the expression \( 7y + 8 - 3(y - 4) \).

1. Distribute the \(-3\) across the terms inside the parentheses:
   \[
   7y + 8 - 3(y - 4) = 7y + 8 - 3y + 12
   \]
   
2. Combine like terms:
   \[
   (7y - 3y) + (8 + 12) = 4y + 20
   \]

So, the simplified expression is \( \boxed{4y + 20} \).

Would you like more details or have any questions about the steps? Here are some related questions:

1. How would you simplify \( 5y - 2(y + 3) + 4 \)?
2. What happens if you change the sign of the \(-3\) in the original problem to \(+3\)?
3. How do you solve the equation \(4y + 20 = 0\)?
4. Can you factor \( 4y + 20 \)?
5. What if the expression had an additional term, say \( -2y \), added at the end?

**Tip:** Always distribute multiplication over subtraction and addition before combining like terms.

Learn how to simplify the algebraic expression 7y + 8 - 3(y - 4) using the distributive property and combining like terms. This step-by-step guide is suitable for students in Grades 6-8, covering core algebra concepts.

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