You can solve this question if you start by drawing three circles and realize how they can intersect in more points.
The result is they can intersect maximum in 6 points: two points between each pair of circles.
After that, you can draw a line that intersect each circumference in two different points. That will make another 6 points.
=> 6 + 6 = 12
Then, the answer is that the largest possible number of intersection points is 12.