We need to subtract #color(red)(3m)# and #color(blue)(2)# from each side of the equation. This will let us isolate the #m# terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

#9m + 2 - color(red)(3m) - color(blue)(2) = 3m - 10 - color(red)(3m) - color(blue)(2)#

#9m - color(red)(3m) + 2 - color(blue)(2) = 3m - color(red)(3m) - 10 - color(blue)(2)#

#9m - color(red)(3m) + 0 = 0 - 10 - color(blue)(2)#

#9m - color(red)(3m) = - 10 - color(blue)(2)#

Next, we can combine like terms on each side of the equation:

#(9 - 3)m = -12#

#6m = -12#

Now we can divide each side of the equation by #color(green)(6)# to solve for #m# and keep the equation balanced:

#(6m)/color(green)(6) = -12/color(green)(6)#

#(color(green)(cancel(color(black)(6)))m)/cancel(color(green)(6)) = -2#

#m = -2#