If there are six straight lines and none are parallel to any other what is the maximum number of intersections there could be?

There can be a maximum of 15 intersections. With two non-parallel lines, there will be one intersection, a third (non-parallel) line can be drawn to cut the other two, and that makes 2 more intersections for a total of 3. You can actually draw this out, and with a fourth, fifth and sixth line, you will create a maximum of 3, 4 and 5 more intersections (respectively), and this will bring your total to fifteentotal intersections for the six lines. You can get each successive line to cut all of the other existing lines if you draw them in a prejudicial (maximized) way.