To simplify this expression, we must first expand the expressions inside the parentheses:

(2-3m)^2 = (2-3m)(2-3m) = 4 - 4(3m) - 3m(2) + 9m^2
= 4 - 12m - 6m + 9m^2
= 4 - 18m + 9m^2

Now let's expand the second term:

(2-3m)(3m+2) = 2(3m) + 2(2) - 3m(3m) - 3m(2)
= 6m + 4 - 9m^2 - 6m

Now substitute these into the original expression:

3(2-3m)^2 - 3(2-3m)(3m+2)
= 3(4 - 18m + 9m^2) - 3(6m + 4 - 9m^2 - 6m)
= 12 - 54m + 27m^2 - 18m - 12 + 27m^2 + 18m
= 27m^2 - 72m + 12

Therefore, the simplified expression is 27m^2 - 72m + 12.