This exercise is from Raymond Murphy's English Grammar in Use. The exercise is to practise using "could have done" and "couldn't have done" (not "could do"!).
Read this information about Ken:
Ken didn't do anything on Saturday evening. Ken doesn't know anything about machines. Ken was free on Monday afternoon. Ken was short of money last week. Ken's car was stolen on Monday. Ken had to work on Friday evening.
Some people wanted Ken to do different things last week but they couldn't contact him. So he didn't do any of these things. You have to say whether he could have done or couldn't have done them.
- Ken's aunt wanted him to drive her to the airport on Tuesday. Answer: He couldn't have driven her to the airport (because his car had been stolen).
The idea is that it would not have been possible for Ken to drive his aunt to the airport, even if she had been able to contact him. "Could do" is not correct. But if we change the context and don't use it in the sense of "it would not have been possible for him to do that" and instead say "Ken's aunt wanted/asked him to drive her to the airport on Tuesday, but he couldn't (drive her ...)", then doesn't that make sense? Is it correct?