Ever since season 3, we know that Daryl never had a chance to say good bye to the people who really mattered in his life until he became a part of the family he found at the quarry outside Atlanta.
His mother died in their burning house when he was nine while he was out playing with the kids from his neighborhood.
Merle died while Daryl was on his way to save him, knowing he intended to go up against the Governor on his own to save his baby brother’s life - and when Daryl arrived at the site he was forced to put down Merle’s walker.
Carol was exiled while he was out on a run for flu meds, so he could neither prevent this, nor go out after her at once while there was still any chance of finding her, nor say good bye to her (if he had approved of the decision, which I cannot believe he would have, had Rick discussed it with him).
He lost Carol again when she felt forced to leave Alexandria for the sake of her own mental health, and since she would have been unable to leave if she had attempted to say good bye to him face to face, she didn’t, but left in secret in the middle of the night, leaving only a letter for her family.
The good bye hug at the Hug Shack was initiated by Daryl as he was leaving because he couldn’t bear the thought of just walking away without showing her, again, how much he loves her and cares for her.
The hug in 8.01 is different in that Carol was already turning toward the car to leave for her part in the mission - but then visibly changed her mind, turned to face Daryl, and walked toward him as he was sitting on his bike to initiate a good bye hug that was completely unexpected, and that I would bet means the world to him.
This is the first explicit “good bye” that Daryl gets in his life from someone leaving, at a moment when they both know that either or both of them might not survive what they are facing. And in this, the hug is exceptional.