We are tasked with solving the equation:

\[
4y - 4 = 2(y - 3)
\]

### Step-by-step solution:

1. **Distribute** the \(2\) on the right side:

\[
4y - 4 = 2y - 6
\]

2. **Move the variable terms** (involving \(y\)) to one side by subtracting \(2y\) from both sides:

\[
4y - 2y - 4 = -6
\]

This simplifies to:

\[
2y - 4 = -6
\]

3. **Move the constant terms** to the other side by adding \(4\) to both sides:

\[
2y = -6 + 4
\]

Simplifies to:

\[
2y = -2
\]

4. **Solve for \(y\)** by dividing both sides by \(2\):

\[
y = \frac{-2}{2} = -1
\]

Thus, the solution is:

\[
y = -1
\]

Would you like more details on any of these steps?

### Related questions:
1. What is the solution to \(3x - 5 = 2x + 7\)?
2. How do you solve \(5y + 8 = 3(y + 2)\)?
3. What are linear equations and how are they solved?
4. How do you check if the solution to a linear equation is correct?
5. Can you explain how to solve equations with variables on both sides?

**Tip:** When solving linear equations, always simplify both sides as much as possible before solving for the variable.

Learn how to solve the linear equation 4y - 4 = 2(y - 3) with a detailed step-by-step solution. This problem introduces the distributive property and solving equations with variables on both sides. Suitable for students in Grades 6-8.

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