We have to define and discuss some vocabulary before answering this question in a satisfactory way. The problem here is that different teachers and texts can use different definitions.
Personally, I prefer to use the term "structures" to refer to all of the contents of a cell, with "organelles" being a somewhat circular definition; if it's found in a prokaryote, it's not an organelle. If it's found only in a eukaryote, then it's an organelle. This is because only eukaryotes have organelles. This definition doesn't really teach you what an organelle is, but it makes it easier to remember when you get to those questions on an assessment that ask "which of these is an organelle?"
The exact definition of an organelle is a bit hazy. Normally it refers to small, specialized, relatively complex structures that perform specific functions within the cell. Well, great, I say to my students, the only problem is that prokaryotes also have small, specialized structures, just not to the same degree that eukaryotes do, and this contradicts the idea that only eukaryotes have them. For example, ribosomes are found in both, and are small and relatively specialized, but because they're found in prokaryotes, they're not considered organelles. Another problem with this is that modern research, more modern than many textbooks, suggest that prokaryotes are more complex than we once thought, and the idea of classifying prokaryotes and these goopy lumps of chaotic junk is outdated.
So, the usual textbook answer to the question is that there are NO organelles common to both prokaryotes and eukaryotes, because prokaryotes do not contain any organelles. If your teacher is going for this baseline, surface-level answer, then you're good.
However, there are several structures common to both. This is why I prefer the term structure, because it eliminates the confusion about whether something counts as an organelle. Common structures include:
- cell membrane
- genetic material