`2/3(9x-6)-4=9x-6`
Based on the equation above, what is the value of 3 x − 2 ?

Options

A. `-4`
B. `-4/5`
C. `-2/3`
D. 4

Explanation

To solve the equation \( \frac{2}{3}(9x - 6) - 4 = 9x - 6 \) and find the value of \( 3x - 2 \), we can follow these steps:

### Step 1: Simplify the left side of the equation
Start with the equation:
\[ \frac{2}{3}(9x - 6) - 4 = 9x - 6 \]

Distribute \( \frac{2}{3} \) to \( (9x - 6) \):
\[ \frac{2}{3} \cdot 9x - \frac{2}{3} \cdot 6 - 4 = 9x - 6 \]
This simplifies to:
\[ 6x - 4 - 4 = 9x - 6 \]
Combining like terms gives:
\[ 6x - 8 = 9x - 6 \]

### Step 2: Rearrange the equation
Now, let's move all terms involving \( x \) to one side and constant terms to the other side:
\[ 6x - 9x = -6 + 8 \]
This simplifies to:
\[ -3x = 2 \]

### Step 3: Solve for \( x \)
Dividing both sides by -3 gives:
\[ x = -\frac{2}{3} \]

### Step 4: Find \( 3x - 2 \)
Now, substitute \( x \) back into the expression \( 3x - 2 \):
\[ 3x - 2 = 3\left(-\frac{2}{3}\right) - 2 \]
This simplifies to:
\[ -2 - 2 = -4 \]

### Final Answer
Thus, the value of \( 3x - 2 \) is:
\[ \boxed{-4} \]