If I have a character (A) that can carry a friendly (B), and that friendly character (B) is next to an opponent character (C), Can (A) carry (B) away from (C) without needing roll a d6 for break away?

The character that is given an action to move is the one that needs to roll for break away. If that character is not adjacent to an opponent, then it does not need to roll for break away. A carried character never has to roll for break away.