If you didn't want to draw, you could notice that both triangles have bases that run along the x-axis. The first triangle has a base that runs from (2,0) to (14,0) and a vertex at (8,12), so that's a base of 12 and a height of 12. The second triangle has a base that runs from (6,0) to (10,0) and a vertex at (8,4), so that's a base of 4 and a height of 4. The second triangle is 1/3 as big in both directions, so it will have 1/9 the area of the first one. (1/3 * 1/3)

Having said all that, most people would probably do best to draw a picture. It doesn't have to be pretty and it should only take a few seconds to make. If it ensures that you visualize the problem correctly, then it's worth it. The step you can skip is actually calculating the areas. You only need to know PQR's area relative to LMN; you don't have to know the actual values.