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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**