The correct option is
A Certainly. What time in the evening?
Here, we have to give the best response to the given question. The question requires a 'yes' or 'no' answer. However, the question doesn't mention the time or the place for dinner, so the listener has to respond or ask accordingly. Let's have a look at the options.
Option A - 'No problem' is used when someone does something inappropriate or apologises and you want to empathize them. Hence, option A is incorrect.
Option B - 'Yes, I am' is a correct response, but it is incomplete. It's a short response, and as the question doesn't specify the time in the evening, one must ask about it. Hence, option B is incorrect.
Option D - 'Why not?' is incorrect, as quoting a question against question is logically incorrect. Also, 'why not?' can be a sarcastic comment. Hence, option D is incorrect.
Option C - Here, 'certainly' means 'okay'. To be really sure about it, the listener must confirm the time by asking 'What time in the evening?'. Hence, option C is correct.