The diagram is shown below
Point A is located at (0,8). It's exactly 8 units away from the origin (0,0).
Let's say point C is at the origin. That would mean segment AC is 8 units long.
Divide segment AC into four equal parts. Each part is 8/4 = 2 units long.
Move to point A(0,8) and then drop down 2 units to arrive at (0,6). Use your straightedge to draw a horizontal line from (0,6) until you reach the diagonal line AB. Mark point P on the diagonal line. Refer to the diagram to see what I mean.
Now move back to (0,6) and drop down another 2 units to get to (0,4). Draw a horizontal line through this point until you reach the diagonal line. Mark point Q on the diagonal line.
Repeat this process until you get to the origin. You'll find that segment AB has been cut into four equal parts. This works because we've divided AC into four equal parts, which helps divide AB into four equal parts. The two concepts are directly connected. More specifically, we're using similar triangles to help do the subdivisions here.
So this trick is very handy if you have a diagonal road you're trying to divide into four (or any number) equal parts. It's also useful if you are dealing with fencing and you want to divide which if your friends will take care of which portions of the fence. Those are just two examples of real world applications.