fejezhettek
fejezhettek is a Hungarian verb form. It is the conditional mood, past tense, third-person plural conjugation of the verb "fejezni". "Fejezni" itself means "to finish", "to end", "to decapitate", or "to top" (in the sense of a plant). Therefore, "fejezhettek" translates to "they could have finished", "they might have ended", "they could have decapitated", or "they might have topped". The specific meaning in a sentence would depend on the context.
The conditional mood in Hungarian expresses possibility, hypothetical situations, or polite requests. The past tense indicates