To determine the number of solutions to the equation \( \frac{2}{3}(6m + 9) - 6 = 4m \), let's simplify and solve it step by step.
Start by distributing the \( \frac{2}{3} \):
\[ \frac{2}{3}(6m) + \frac{2}{3}(9) - 6 = 4m \]
This simplifies to:
\[ 4m + 6 - 6 = 4m \]
The +6 and -6 cancel out:
\[ 4m = 4m \]
This equation \( 4m = 4m \) is true for all values of \( m \). Therefore, it indicates that there are infinite/many solutions.
So the correct answer is:
infinite/many solutions