can't是不可能的意思.例：I can't move that box because it is so heavy.
don't是助动词.例：I don't know.
did't是don't的过去式,在一般过去式的句子中改否定句是常用到.例：He worked out this problem by himself.的否定句是He didn't work out this problem by himself.
couldn't是can't的过去式.could也有时候表示委婉语气.例：Could you give me that pen?