"I do not work on Wednesday."
Translation:Szerdán nem dolgozom.
The correct solution is here "dolgozom". A lot of hungarians use "dolgozok" but it is not really correct in Hungarian. (See: Andreas305)
Is this a sentence that can use either the definite or the indefinite conjugation?
You surely ask because "dolgozok" and "dolgozom" is accepted.
No, you have to use indefinite conjugation. But "dolgozni" is a so called ik-verb. In the third person singular present tense this verb has the suffix -ik - while usual verbs have no suffix.
And all those verbs usually use the suffix -om/ -em / -öm for the first person singular present tense as in definitve as in indefinite conjugation.
But: a lot of Hungarians prefer using for ik-verbs in the first person singular present tense the suffix -ok / -ek / -ök. And it seems to be accepted in the colloquial language while it is wrong grammatically. So, Duolingo seems to be very colloquial - at least in this case ;-)