A characteristic that organisms in domain Eukarya share is that they have cell structures with membranes. Specifically, eukaryotic cells have membrane-bound organelles, such as a nucleus, mitochondria, and endoplasmic reticulum.
From your provided options, while none directly states this, the closest inference is to reject the other answers as they contain inaccuracies regarding cellular structures:
- They have cell structures without membranes. (Incorrect)
- They are multicellular. (Incorrect, as some eukaryotes are unicellular, such as yeast and protists)
- They lack cell structures and membranes. (Incorrect)
- They are unicellular. (Incorrect, as eukaryotes can be unicellular or multicellular)
None of the given options correctly describes Eukarya; however, the defining characteristic could be described as having membrane-bound organelles or structures.