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

Here is Why You Need An Adapter

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

Anguilla

In Anguilla, outlets of type A and B are in use.

Type A

Type B

Bhutan

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

Type C

Type D

Type G