Case1. You don't know how to explain.
어떻게 설명해야 하지?
formal(If someone is older than you): 어떻게 설명해야할까요?
case2. If you try to say sarcastically. For example, other people talk a lot and you couldn't get a time for explaining something.
내가 어떻게 설명을 할 수가 있니?
formal : 제가 어떻게 설명을 할 수 있을까요?