Learn Russian: Я как раз перепутал их отпечатки!

While только что refers to time ("just a moment ago"), как раз means "exactly," "as it happens," or "precisely." Here, the speaker is using как раз to emphasize the irony or the exactness of the situation—meaning "That is exactly what I happened to do!" rather than "I did it a second ago."

Could I use перепутал to say that a complicated explanation confused me?

No, перепутал specifically means you mistakenly switched or "mixed up" two or more distinct things (like fingerprints, twins, or dates). If you are mentally confused by a difficult explanation, you would use the reflexive запутался (got tangled up/confused).

What does the prefix пере- add to the base verb путать?

The imperfective verb путать means to tangle or muddle. The prefix пере- often carries the idea of crossing over or exchanging. Here, it creates the perfective meaning of getting items completely "crossed" or swapped with each other.

The English translation says "fingerprints", but the Russian word for "fingers" is missing. Is that normal?

Yes! The full official term is отпечатки пальцев (prints of fingers), but in a clear context like an investigation, Russians shorten it to отпечатки, exactly how we just say "prints" in English. The word itself comes from печать (a stamp or seal).