You Do Need power plug adapter while traveling from New Caledonia to Equatorial Guinea.

Here is Why You Need An Adapter

The outlet and plug type used in Equatorial Guinea are C and E and in New Caledonia are C and F. This is how they look like.

New Caledonia

In New Caledonia, outlets of type C and F are in use.

Type C

Type F

Equatorial Guinea

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

Type C

Type E