Explain why three coplanar lines may have zero, one, two, or three points of intersection?

If all three lines are parallel, there are zero points of intersection. If all three lines go through a point, there is one point of intersection. If two lines are parallel and the third one crosses them, there are two. If the three lines make a triangle, there are three points. Not unless they're collinear, in which case they intersect an infinite number of times.