Let's solve the equation step by step.

### Given equation:
\[
2(3x + 3) - 4(2x - 1) = 6x + 6
\]

### Step 1: Distribute the terms.
Distribute the constants outside the parentheses:

\[
2(3x + 3) = 6x + 6
\]
\[
-4(2x - 1) = -8x + 4
\]

Now substitute these back into the equation:

\[
6x + 6 - 8x + 4 = 6x + 6
\]

### Step 2: Combine like terms.
On the left-hand side, combine the \(x\)-terms and the constant terms:

\[
(6x - 8x) + (6 + 4) = 6x + 6
\]
\[
-2x + 10 = 6x + 6
\]

### Step 3: Move all \(x\)-terms to one side.
Add \(2x\) to both sides:

\[
-2x + 10 + 2x = 6x + 6 + 2x
\]
\[
10 = 8x + 6
\]

### Step 4: Solve for \(x\).
Subtract 6 from both sides:

\[
10 - 6 = 8x
\]
\[
4 = 8x
\]

Now, divide both sides by 8:

\[
x = \frac{4}{8} = \frac{1}{2}
\]

### Final answer:
\[
x = \frac{1}{2}
\]

Do you need any details or further explanation on a step? 

Here are 5 related questions to consider:

1. How would you solve if the right side were different, like \(6x - 6\)?
2. Can you explain why distributing first makes the problem easier to solve?
3. What happens if you move the constants before combining like terms?
4. How do you handle equations with fractions at the beginning?
5. Can this method be applied to solve equations with inequalities?

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

Step-by-step solution to the linear equation 2(3x+3)-4(2x-1)=6x+6. This problem involves applying the distributive property and combining like terms. Ideal for students in Grades 7-9 learning how to solve linear equations.

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