When you feel sympathy for someone, you actually have the feeling of compassion, sorrow, or pity for the troubles or problems that another person has. Empathy is a much "deeper" feeling, it basically means that you "putt yourself in the shoes" of another, you feel what they feel. Sympathy allows you certain distance from the other person, so to say. It is usually believed that not everyone is capable of empathy. So B, empathy :)

Sympathy is feeling compassion, sorrow, or pity for the hardships that another person encounters, while empathy is putting yourself in the shoes of another. She was always in perfect "empathy" with me with regard to my love of nature.

If you feel sympathy, you simply feel sorry for somebody. You might feel sorry for somebody because they are upset, but without knowing or understanding why they are upset. If you feel empathy with somebody, then this means that you can relate to (understand) their actual feelings. Some people feel so much empathy for other people that it affects their ability to live their own lives - for example, if you are a counsellor (somebody that allows other people to talk to them about their problems) it is possible to become upset yourself as you feel the emotions that your client is feeling.

The test question has obviously been taken from the following passage from W. H. Hudson’s “Far Away and Long Ago”: “I never spoke of these feelings to others, not even to my mother, notwithstanding that she was always in perfect sympathy with me with regard to my love of nature.” Sympathy can mean “feelings of pity and sorrow for someone else's misfortune”, but it also has another meaning: “understanding between people; common feeling” (https://en.oxforddictionaries.com/definition/sympathy) I believe it’s this meaning of “sympathy” that is used in the text quoted above. To me it’s the only thing that makes sense. In my opinion the test question is a terrible question. I have now seen many such poor test questions. It seems that especially Chinese learners of English use terrible teaching materials made by incompetent people. “Far Away and Long Ago” was written in 1918. You can’t just take a sentence from an old book and remove it from all context and then use it as the basis for a test question. It’s ridiculous in my opinion. I strongly recommend that you don’t use the book/material from where you have this question again. When native speakers don’t even understand the question, how can a Chinese learner then possibly understand it?

I'm just going to give my personal answer as US native speaker. When I feel sympathy, I am still viewing the situation from the outside. When I feel empathy, I actually am role-playing the other person in my mind. For example: I'm a man. When my wife tells me about the labor pains she experienced giving birth, I can feel sympathy, but I can't experience empathy because I've never experienced labor pains. However, when she tells me about the pain she had from a kidney stone, I've had a kidney stone myself and I can experience empathy! (Ow!) I'm glad Mikkel found the original context, and I agree with him that it is a terrible question. It is as if the test writer looked for a passage containing the word "sympathy" and didn't actually understand the way the word was being used themselves. However, as a fairly good "test-taker" I think I would have chosen "sympathy" as the correct answer because it is a possible fit and I don't think empathy is.