Final answer:
Barry's parenting style is permissive or indulgent, allowing his son to make his own decisions without much guidance or involvement.
Step-by-step explanation:
Barry's parenting style in this situation seems to be permissive or indulgent. A permissive or indulgent parenting style is characterized by lenient rules and lack of discipline. In this case, Barry's response of 'sure, whatever' suggests that he is allowing his son to make his own decisions without much guidance or involvement.