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To determine the number of solutions for the equation \(\frac{2}{3}(6m + 9) - 6 = 4m\), we will first simplify the left side of the equation.
1. Distribute \(\frac{2}{3}\):
\[
\frac{2}{3}(6m) + \frac{2}{3}(9) - 6
\]
This simplifies to:
\[
4m + 6 - 6
\]
which further simplifies to:
\[
4m
\]
2. Now we have the equation:
\[
4m = 4m
\]
This equation is true for all values of \(m\) since both sides are identical.
Thus, there are **infinite solutions** to the equation.
The correct response is: **infinite/many solutions**.