This was indeed a gem of a puzzle, and the more I have thought about it, the more I like it. Thanks again to Girish Tutakne for sharing this puzzle. I received a few correct answers – Suman Saraf, Prakhar Prakash, Pratik Poddar, Raghu and Abhinav Jain – well done all!

The reason why most people were stumped by this question is that they assume that they assume that the small coin has to traverse the circumference of the bigger coin, which is 2*pi*6. Since the circumference of the smaller coin is 2*pi*2, the answer must be 3.

The best way to try this puzzle is to do this puzzle with two coins of identical size. With he logic above, there should be only one rotation, however, as you will see there are two. The reason is that the rotating coin is rotating in a circle with the radius that is equal to the sum of the radii. Therefore in the case of this puzzle, it is rotating around a circle with the radius 6+2 = 8 cm, and hence needs to rotate 4 times.

Here is a video link that already existed on YouTube for this puzzle.

Hope you all enjoyed the puzzle!