I live in two story duplex where both units have the bathrooms on the second floor. When my neighbor uses the sink, my sink fills with water. Why?

Your sinks are probably back to back and drain into the same drain line. There is a blockage or partial blockage in the main drain line for the sinks. When you use your sink it probably backs up into their sink.

One of you needs to snake the drain line. Plunging won't do any good because you will have to block the drain and overflow in one sink while you plunge the other. You could try, but you need to have the neighbor block their drain and overflow and you block your overflow and plunge.

As said above: you share common drain with your neighbor. Drain blockage is in common part of the drain. Snake one, fix problem for both sides. Do as suggested above

Milo