The maximum number of points into which 4 circles and 4straight lines intersect, is

4 lines intersect each other in _{${}^4{C}_2=6$}  points. 4 circles intersect each other in _{$2{\times }^4{C}_2=12$}  points. Further, one line and one circle intersect in two points. So, 4 lines will intersect four circles in 32 points.

_$\therefore$  Maximum number of points _{$=6+12+32=50.$}