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

Here is Why You Need An Adapter

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

Palestine

In Palestine, outlets of type C and H are in use.

Type C

Type H

Anguilla

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

Type A

Type B