Show how three lines in a plane can intersect in no points, exactly one point, exactly two points, or exactly three points?Draw it

Drawing a picture will be the easiest way to picture the
four scenarios that you are describing.  It will be easiest to visualize if you draw a
separate diagram for each of the four scenarios.

In the
first scenario you are asked to show how three lines in a plane can intersect in no
points.  If three lines within the same plane are parallel,  they will not intersect. To
draw this, you should first draw a plane, usually represented by a parallelogram. 
Within the plane, draw three parallel lines.

In the second
scenario you are asked to show how three lines can intersect in one points.  In this
case, your lines will all cross in one location, similar to an
asterisk.

In the third scenario you are asked to show how
two lines cam intersect in two points.  In this case, you will need two parallel lines
and a third line that intersects both of the parallel
lines.

In the fourth scenario you are asked to show how
three lines can intersect in three points.  In this case you need to show three lines
forming a triangle with the ends of the lines extended beyond the three corners of the
triangle. 

I hope that these descriptions help you see the
final results.