érvényesíthessék
érvényesíthessék is a Hungarian verb form. It is the conditional, plural, third-person, subjective mood of the verb érvényesít, which generally translates to "to assert," "to enforce," "to validate," or "to realize."
Breaking down the word, "érvényes" means valid or in effect. The suffix "-ít" often indicates causation, so
Therefore, "érvényesíthessék" translates to "that they might be able to assert," "that they might be able to