3[2m-6]=3m-9

You were going pretty good, Complex, until after this step

6m - 18 =  3m - 9      add18 to both sides........subtract 3m from both sides

3m = 9                      divide both sides by 3

m = 3

Check this solution in the original problem to see that it "works"

Ok lets see...

$3[2m-6]=3m-9$

$[6m-18]=3m-9$

$3m-6=-9$

$3m = -3$

$m=-1$

Hoped that helped...

-Complex