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.