Use a short knife.

Cut the two ends off as shown

Slit the peels all around, about an inch apart. Make sure to slit only the peels; dont cut the pulp

Barely separate the peels from the pulp at one end using a knife as shown.

Like this (see the slits and the separation?)

Push your thumb through the separation and down all the way to the other end

That's one portion off! The slits over the peels enable you to peel a portion at a time, making it very easy

Peel off the white fibre using a knife. While the fibre is good for you, it has a slightly bitter taste that I'm not fond of..

Peeled and cleaned perfectly :) It's easy and very quick!

How to neatly and easily peel oranges with thick peels

Oranges with thick peels can be difficult to peel. Here's how you can do it without hurting your fingers or peeling messily with a knife