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

Here is Why You Need An Adapter

The outlet and plug type used in Anguilla are A and B and in Mongolia are C and E. This is how they look like.

Mongolia

In Mongolia, outlets of type C and E are in use.

Type C

Type E

Anguilla

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

Type A

Type B