Below is a diagram of the right Kan Extension. Then I drew both left and right extensions in one diagram to emphasize the difference.

![Right Kan Extension](http://aether.co.kr/images/right_kan_extension.svg)
![Left and Right Kan Extension](http://aether.co.kr/images/left_right_kan_extension.svg)

**Puzzle 160**
![Right Kan Extension natural transformation](http://aether.co.kr/images/kan_extension_example_2.svg)

There are \\(4^5\\) natural transformations for both \\(\alpha\\) and \\(\beta\\).

Edit: I mislabeled the category of \\(H\\) and \\(F \circ G\\). Now its fixed.