To determine how many solutions the equation \( \frac{2}{3}(6m + 9) - 6 = 4m \) has, we will simplify and solve the equation step by step.
- First, distribute \( \frac{2}{3} \) to \( (6m + 9) \):
\[ \frac{2}{3}(6m) + \frac{2}{3}(9) = 4m + 6 \]
So, we can rewrite the equation:
\[ 4m + 6 - 6 = 4m \]
- Simplify the left side:
\[ 4m + 6 - 6 = 4m \] \[ 4m = 4m \]
This expression holds true for all values of \( m \).
Since every value of \( m \) satisfies the equation, this means that there are infinitely many solutions.
Thus, the equation \( \frac{2}{3}(6m + 9) - 6 = 4m \) has infinitely many solutions.