Answer
The ways that eukaryotes control gene expression include alternative splicing, regulation of chromatin configuration, altering mRNA movement out of the nucleus, small RNA's, and protein degradation directed by ubiquitin. The first three are unique to eukaryotes and could not be done by prokayotes which lack needed features such as introns (splicing) or a nucleus (transport of mRNA). The last two could operate in prokaryotes, at least in theory, though it would require an actual test to see if they did, indeed, work there.
Work Step by Step
To get to this answer, make a list of the ways that eukaryotic cells regulate gene expression, and then consider which ones are unique to eukaryotes because they either involve eukaryotic organelles which prokaryotes lack (such as mRNA transport out of the nucleus) or steps which prokaryotes lack (splicing).
