#3|6m -4|<=12#

Let start by dividing both sides by #color(red)(3)#

#(cancel3(|6m -4|))/cancelcolor(red)(3) <= 12/color(red)(3)#

#|6m - 4| <= 4#

We know...

#6m - 4<=4 and 6m - 4>= -4#

Let start with the first condition

#6m - 4 <=4#

Add #color(red)(4)# to both sides

#6m cancel(- 4) cancelcolor(red)(+4) <= 4 color(red)(+4)#

#6m <=8#

Divide both sides by #color(red)(6)# to find #m#

#(cancel6 m)/cancelcolor(red)(6) <= 8/color(red)(6)#

#m <= 4/3#

Now let solve the second condition

#6m - 4 >= -4#

Add #color(red)(4)# to both sides

#6m cancel(-4) cancelcolor(red)(+4) >= cancel(-4) cancelcolor(red)(+4)#

#6m >= 0#

Divide both sides by #color(red)(6)#

#(cancel6m)/cancelcolor(red)(6) >= 0/color(red)(6)#

#m >=0#

Thus,

the final answers are #m <=4/3 and m>=0#