To solve the equation \( 600m - \frac{3}{5} = 600m - \frac{2}{6} \), let's first simplify the fraction \( \frac{2}{6} \):
\[ \frac{2}{6} = \frac{1}{3} \]
Now, rewrite the equation:
\[ 600m - \frac{3}{5} = 600m - \frac{1}{3} \]
Next, we can eliminate \( 600m \) from both sides:
\[ -\frac{3}{5} = -\frac{1}{3} \]
Now, multiply both sides by -1:
\[ \frac{3}{5} = \frac{1}{3} \]
Since \( \frac{3}{5} \) does not equal \( \frac{1}{3} \), we see that there is no solution to the original equation as it leads to a contradiction.
Thus, the final answer is that there is no solution to the equation.