Empathy is very strong sympathy so that you feel the other person’s pain when they stub their toe.
Write something in which you make images for how it feels to he ‘one’ with somebody or something.
Or think of some way of creating a conversation which ‘shows’ this between people without saying it.
Or you might represent a situation where there’s a lack of empathy, or a false kind of ‘I understand’. Or, of course, there are some people who are unable to feel empathy, miss the ‘signs’, are in a sense locked in their own perceptions. Then there’s the situation of illusory empathy. You think he/she is deeply ‘there’, but no. . .
You might want to link this technically or otherwise with the need for the writer to have empathy with his/her characters, to ‘be’ them in some sense, rather as some forms of stage and film acting require. One way of showing this is to show the way in which one person is able, as it were, to ‘carry on’ another’s thought.
This links to the mirror theme. How is empathy different from merely reflecting, or being reflected, in someone like you?
Then consider whether empathy has to be total. You can empathise with your partner and he/she with you, and yet he/she keeps some things secret, a past, a lover, a fear.