Let's solve the equation step by step:

\[
-6(y - 2) = 4(y - 9)
\]

### Step 1: Distribute on both sides
Distribute \(-6\) and \(4\) to the terms inside the parentheses:

\[
-6 \cdot y + 12 = 4 \cdot y - 36
\]

This simplifies to:

\[
-6y + 12 = 4y - 36
\]

### Step 2: Move all terms involving \(y\) to one side
Add \(6y\) to both sides to bring the \(y\)-terms together:

\[
12 = 10y - 36
\]

### Step 3: Move the constant terms to the other side
Add 36 to both sides to move the constant to the other side:

\[
48 = 10y
\]

### Step 4: Solve for \(y\)
Now, divide both sides by 10:

\[
y = \frac{48}{10} = 4.8
\]

Thus, the solution is:

\[
y = 4.8
\]

Would you like a detailed explanation of any step or have any further questions?

Here are 5 related questions for practice:
1. Solve \(-5(x + 3) = 2(x - 4)\).
2. Solve \(7(2x - 1) = 3(x + 4)\).
3. If \(-3(y - 5) = 9(y + 2)\), what is \(y\)?
4. Solve for \(y\): \(4(3y + 1) = 5(y - 6)\).
5. What is the solution to \(-8(x - 7) = 5(x + 2)\)?

**Tip:** Always distribute carefully when solving equations with parentheses to avoid mistakes.

Explore how to solve the linear equation -6(y-2) = 4(y-9) step-by-step using the distributive property. This problem includes key algebraic concepts and demonstrates how to handle equations with parentheses. Perfect for students in Grades 6-8.

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