Choose the appropriate variant. ... they ... on Saturdays?

The correct answer is:

Do ... work

Полный вариант вопроса: Do they work on Saturdays? (Они работают по субботам?)

Explanation:

We should use the Present Simple tense to ask about habitual actions. The question form is:

Do/Does + subject + verb (infinitive)

With the subject "they" we use "Do" and the infinitive form of the verb "work".