Suspension has been lifted but still have all the reprocautions

You do not have a permanent suspension. By the looks of it, you had a communications suspension on 6/22 that has already been lifted. If the suspension was still in place it would have a date for when it ends.

My suspension was suppose to be lifted on 12/6/2015 6:49pm eastern time and has not been lifted yet. It was a communication suspension and I can't talk in party's at all. Can you help?

First check the enforcement site to verify that all suspensions are really over: https://enforcement.xbox.com/en-US

If all suspensions are expired, and you are therefore clear, try the following steps:

1. Remove your account from the Xbox.
2. Give your Xbox a power cycle.
3. Add your account back into the Xbox.
4. Attempt to use the social features now.

Bans or suspensions will not be lifted until the date that has been stated

Suspensions are lifted at approximately the same time of day as they are enforced. So even though it is the 27th, it probably still hasn't been lifted yet.