Assuming the lines need to be straight, I'd go with a triangle (the lines can keep going to infinity too, that's fine). But that only has 3 intersections of 2 lines, if you need all 3 lines to intersect exactly 3 times and need to be straight, it can't be done, I don't think. However, you could lay each line on top of each other to have infinite intersection points, but that's probably not what they want.
