Let's solve the equation \( \frac{2}{3}(3m + 9) = -2(2m + 6) \).

### Step 1: Distribute the terms on both sides.
On the left-hand side, distribute \( \frac{2}{3} \) over \( (3m + 9) \):

\[
\frac{2}{3}(3m) + \frac{2}{3}(9) = 2m + 6
\]

This simplifies to:

\[
2m + 6 = -2(2m + 6)
\]

Now, on the right-hand side, distribute \( -2 \) over \( (2m + 6) \):

\[
-2(2m) - 2(6) = -4m - 12
\]

So the equation now is:

\[
2m + 6 = -4m - 12
\]

### Step 2: Move all terms involving \( m \) to one side of the equation and constants to the other side.

Add \( 4m \) to both sides:

\[
2m + 4m + 6 = -12
\]

Simplify:

\[
6m + 6 = -12
\]

### Step 3: Move the constant term to the other side.

Subtract 6 from both sides:

\[
6m = -12 - 6
\]

\[
6m = -18
\]

### Step 4: Solve for \( m \).

Divide both sides by 6:

\[
m = \frac{-18}{6}
\]

\[
m = -3
\]

So the solution is \( m = -3 \).

---

Do you want further details or explanations? Here are some related questions to deepen understanding:

1. What happens when you divide by a negative number?
2. How do you solve equations involving fractions?
3. What are some methods to check if the solution is correct?
4. Can you explain how distributing works in algebra?
5. What is the significance of moving variables to one side?

**Tip:** Always check your solution by substituting it back into the original equation!

Learn how to solve the linear equation 2/3 (3m+9) = -2 (2m+6) step-by-step. This problem covers key algebra concepts such as distribution and moving variables. Suitable for students in Grades 8-10.

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