The given equation is:

\[
4(3y + 5) = y - 8(-y - 4)
\]

Let's solve this step by step.

### Step 1: Expand both sides
First, distribute the terms inside the parentheses on both sides:

\[
4(3y + 5) = 4 \cdot 3y + 4 \cdot 5 = 12y + 20
\]

On the right side:

\[
y - 8(-y - 4) = y + 8y + 32 = 9y + 32
\]

So, the equation becomes:

\[
12y + 20 = 9y + 32
\]

### Step 2: Move all the terms involving \(y\) to one side
Subtract \(9y\) from both sides:

\[
12y - 9y + 20 = 32
\]

This simplifies to:

\[
3y + 20 = 32
\]

### Step 3: Solve for \(y\)
Subtract 20 from both sides:

\[
3y = 12
\]

Now, divide both sides by 3:

\[
y = 4
\]

### Final Answer:
\[
y = 4
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you solve equations with variables on both sides?
2. What is the distributive property in algebra?
3. Can you show how to check the solution by substituting \(y = 4\) back into the original equation?
4. What is the next step if the variable had a fraction in the solution?
5. How do you handle equations with parentheses and negative signs?

**Tip:** Always double-check your solution by plugging the value of the variable back into the original equation!

Step-by-step solution to the linear equation 4(3y + 5) = y - 8(-y - 4). Learn how to apply the distributive property and solve for y. Ideal for students in Grades 8-10 studying algebra and linear equations.

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