You Do Need power plug adapter while traveling from Palau to Libya.

Here is Why You Need An Adapter

The outlet and plug type used in Libya are C and L and in Palau are A and B. This is how they look like.

Palau

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

Type A

Type B

Libya

In Libya, outlets of type C and L are in use.

Type C

Type L