I did it out, and this is the steps I got:
(m - 2) - 5 = 8 - 2(m - 4)
get rid of the parenthesis and distribute:
m - 2 - 5 = 8 - 2m + 8
simplify:
m - 7 = 16 - 2m
add 7 on both sides:
m = 23 - 2m
add 2m on both sides:
3m = 23
after that, to isolate the m, divide both sides by 3 to get your final answer of:
m = 23/3, or 7 and 2/3
hope this helped!