could Could can be used in many different ways, to ask for permission, to make a request or to express ability when referring to the past. Was able to is sometimes used as an alternative to could when we are discussing ability or possibility. We tend to use could when we are talking about ability generally. Compare the following: By the time she was seven, she could already speak three languages. was able to / managed to We tend to use was able to or managed to if we are talking about what happened in a particular situation or are referring to a specific achievement: Were you able to / Did you manage to speak to him before he left home? ~ No, I'm sorry, I wasn't able to / didn't manage to reach him. The fog came down and I wasn't able to / didn't manage to get to the top of the mountain. My brother wanted to carry on, but we managed to / were able to talk him out of it. However, with verbs that refer to the five senses, see, hear, smell, feel, taste, and with verbs that refer to thought processes, understand, believe, remember, decide, we normally use could, even when we are talking about specific occasions: He was standing very close to me and I could smell the garlic on his breath. He asked me when Julie's birthday was, but I couldn't remember. I couldn't decide whether to ask him for a lift or not. I could see that he'd been running.

ur teacher is right

Yes, it's. According to the context, in that cases you would be better to use "to be able to" construction.

sadly, I do not agree with your teacher. I was able to understand. I could understand. See, can= to be able to do something. so, you can use them as per your wish.