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

Here is Why You Need An Adapter

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

Barbados

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

Type A

Type B

Palestine

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

Type C

Type H