You Do Need power plug adapter while traveling from Azerbaijan to Bhutan.

Here is Why You Need An Adapter

The outlet and plug type used in Bhutan are C, D and G and in Azerbaijan are C and F. This is how they look like.

Azerbaijan

In Azerbaijan, outlets of type C and F are in use.

Type C

Type F

Bhutan

In Bhutan, outlets of type C, D and G are in use.

Type C

Type D

Type G