Three different circles and one line intersect each other. what is the largest possible number of intersection points

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.