Maximum points of intersection!

If you select any two circles, you can have max 2 points of intersection. =(5c2)(2). If u select any two straight lines then you have max one point of intersection =( 8c2)(1). And if u select one circle and one straight line you get max 2 points of intersection =(8c1)(5c1)(2). hence total points add up to 20 +28 + 80= 128

This is the same reasoning as Puneet Sharma's answer, just using LaTeX to make it visually clearer

$2$ circles intersect each other at most $2$ times. The number of circle intersections is equal to $2$ times the number of circle pairs, $2\times\binom{5}{2}=2\times10=20$

$2$ lines intersect each other at most $1$ time. The number of line intersections is equal to $1$ times the number of line pairs, $1\times\binom{8}{2}=1\times28=28$

Lastly, a line and a circle intersect at most $2$ times. The number of line and circle intersections is equal to $2$ times the number of line and circle pairs, $2\times5\times8=80$

$20+28+80=128$