Let's solve the equation step by step:

### Given:
\[
12 - (4y + 8) = 0.5(8y - 16)
\]

### Step 1: Distribute both sides

First, distribute the terms inside the parentheses:

\[
12 - 4y - 8 = 0.5 \times 8y - 0.5 \times 16
\]

This simplifies to:

\[
(12 - 8) - 4y = 4y - 8
\]

\[
4 - 4y = 4y - 8
\]

### Step 2: Combine like terms

Now, let's move all the \(y\) terms to one side and the constants to the other side:

\[
4 + 8 = 4y + 4y
\]

\[
12 = 8y
\]

### Step 3: Solve for \(y\)

Now, solve for \(y\) by dividing both sides by 8:

\[
y = \frac{12}{8} = \frac{3}{2} = 1.5
\]

### Final Answer:
\[
y = 1.5
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the solution change if the equation were \(12 - (4y + 8) = 0.25(8y - 16)\)?
2. What happens if you add a constant term to both sides of the equation?
3. Can you solve for \(y\) when the equation includes a quadratic term, like \(y^2\)?
4. What if \(0.5\) were replaced by a different fraction or decimal in the equation?
5. How would you graph both sides of the equation to find the solution visually?

**Tip**: When solving equations, always simplify each side fully before moving terms across the equals sign!

Discover how to solve the linear equation 12 - (4y + 8) = 0.5(8y - 16) with step-by-step instructions. This solution involves using the distributive property and rearranging terms to find y = 1.5. Suitable for students in Grades 8-10, this example covers core algebra concepts like linear equations and equality.

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