In the plane, six lines are drawn such that such that no three of them meet at one point. Can it happen that there are exactly (a) 12 (b) 16 intersection points where two lines meet?
(a) The answer is yes. Some pairs of lines must be parallel. One of several solutions is shown.

(b) The answer is no. Label the lines $a, b, c, d, e, f$. Since two lines cannot meet at more than one point, each intersection point comes from a unique pair of lines:

$$
a b, a c, a d, a e, a f, b c, b d, b e, b f, c d, c e, c f, d e, d f, e f .
$$

There are only 15 pairs. Thus there cannot be 16 points of intersection.