First, if y= |6x| then your graph is wrong. You have y= 6x.
Because both |6x| and are even functions, the graphs are symmetric about the y-axis and I would recommend just integrating on one side then doubling. For x> 0, |6x|= 6x so the two graphs will cross, on the right, when which is the same as . The only positive root of that is x= 7 so the area is .
If it really is y= 6x rather than y= |6x|, just integrate . You don't need to worry about changing signs because 6x is always larger than on that interval so is always positive.