Yes, your answer is correct. In the sentence "Would you care for a cup of coffee?", the subject is "you". The subject is the person or thing that performs the action or is being described in a sentence. In this case, the subject "you" is the one who is being asked if they would like a cup of coffee. The verb "care" shows the action or feeling, and it is performed by the subject, "you". Therefore, "you" is the subject of the sentence.
