You Do Need power plug adapter while traveling from Nepal to Ecuador.

Here is Why You Need An Adapter

The outlet and plug type used in Ecuador are A and B and in Nepal are C, D and M. This is how they look like.

Nepal

In Nepal, outlets of type C, D and M are in use.

Type C

Type D

Type M

Ecuador

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

Type A

Type B