어떻게 V-는 게 좋을까요?
ask how it would be best to proceed
Form
어떻게 + V-는 게 좋을까요? — literally “in what way would it be good to V?” Here, 하다 is generic: 어떻게 하는 게 좋을까요?
Function
Asks what manner or course of action would be preferable. When several options are available, it can naturally mean “How should we proceed? / What would be the best way to handle this?”
Why this form?
뭘 하는 게 좋을까요? — “what would be good to do?”: mainly asks which action to choose. 어떻게 하는 게 좋을까요? — “how would it be best to proceed?”: frames the answer more as a manner or strategy. The two can overlap in an open decision, but they foreground different things.
어떻게 해야 할까요? — “how should we do it / what should we do?”: expresses necessity or solution-seeking more directly; -는 게 좋을까요? evaluates the options in terms of what would be best.
Forms not to confuse
뭘 하는 게 좋을까요?
주말에는 뭘 하는 게 좋을까요? — What would be good to do this weekend?
어떻게 해야 할까요?
이 문제는 어떻게 해야 할까요? — How should we handle this problem?
Examples
그럼 지금 어떻게 하는 게 좋을까요? — So how would it be best to proceed now?
이 상황에서는 어떻게 하는 게 좋을까요? — What is the best way to proceed in this situation?