Here's how to unsync your contacts with Facebook on your Nokia Lumia 820:
(Please note - your Facebook contacts can only be unsynchronised by deleting the email account linked to Facebook. Alternatively, you can hide your Facebook contacts within the People settings.)
- From the Start screen, swipe to the left.
- Scroll down to and tap Settings.
- Tap email + accounts.
- Tap and hold the Facebook account to be deleted.
- Tap delete.
- Tap delete again.
That's it - your Facebook contacts have been removed from your Nokia Lumia 820.