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

Here is Why You Need An Adapter

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

Bhutan

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

Type C

Type D

Type G

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K