What do eukarya and bacteria have in common?
These are both domains.
Domain eukarya contains all eukaryotes; single celled or multicellular organisms with membrane bound organelles especially the nucleus. The Kingdoms in this domain are Plantae, Fungi, Protista, and Anamalia.
Domain Bacteria contains Kingdom Eubacteria
Domain Archea contains Kingdom Archeabacteria.
Kingdom Eubacteria and Kingdom Archeabacteria used to be combined as Kingdom Monera. They are single celled prokaryotes.