You have answered your own question! The reasoning is correct.
200=4m+18-2m,
200=2m+18 (combine like terms on the right-hand side).
Subtract 18 from each side (maintaining equality by taking equal amounts from each side):
182=2m,
Divide each side by 2 (maintaining equality by dividing by an equal amount on each side):
91=m which can also be written m=91 because the amounts on either side are equal.