The correct answer is A. for.
The word “aching” suggests that the person is feeling a deep emotional pain, which is often associated with loneliness. The word “love” suggests that the person is missing someone they care about. The word “for” is the most logical preposition to use in this context, as it indicates that the person is longing for someone.
The other options are not as logical. The word “in” could be used to describe someone who is physically in a place where they feel lonely, but it does not make sense to say that someone is “in love.” The word “about” could be used to describe someone who is thinking about love, but it does not make sense to say that someone is “about love.” The word “with” could be used to describe someone who is accompanied by someone they love, but it does not make sense to say that someone is “with love.”