Question

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**