the greatest possible no. of points of intersection of 8 straight line and 4 circles is

8 Straight lines can have 8C2 points of intersection. Points of intersection of straight lines and circles would be 2*8C1*4c1. Points of intersection between two circles would be 2*4c2. So total number of points of intersection would be sum of all these.
Hope that clears our doubt.
Thanks.

In the question, it hasn't been specified that lines and circles are distinct. this would mean that there are infinite numbers of intersection point. Lets take the case when all the figures are distinct.
There are 3 types of intersection, Circle-line, line-line, circle-circle. Circe-circle can intersect at max 2 points, line-line at 1, and line-circle at 2.
Number of C-C intersections would be-
4C2 X 2 (multiplied by 2 because max intersection for 2 circle is 2)
L-L-> 8C2
L-C-> 8C1 X 4C1 X 2 (multiplied by 2 because intersection for Line and circle can be max 2)
So, the answer is,

4C2 X 2 + 8C2 + 8C1 X 4C1 X 2