How do scientists choose the kingdom in which a eukaryote belongs in?

Well, a eukaryote is an organism with more complex cells. They have a nucleus whereas Prokaryote are unicellular. You can classify which kingdom a eukaryote goes into by singeling out the kingdoms in which prokaryote organisms are found.

Eukaryotic cells are a lot more complex. They have a nucleus in a nuclear membrane, where DNA or other genetic information is stored, as well as lots of organelles that serve different functions.