Learn Dutch: Zij moest vorig jaar in de fabriek werken. - She had to work in the factory last year.

English doesn't have a past tense word for "must", so we use "had to". In Dutch, the verb moeten (to have to / must) does have a past tense. Because the subject Zij (she) is singular, we use the singular simple past form moest.

Why is werken at the very end of the sentence?

When you use a modal verb like moest, the second verb in the sentence gets pushed to the very end in its full dictionary form (the infinitive). Here, moest is the modal verb carrying the time, and werken is the main action.

Could I change the order to "Zij moest in de fabriek vorig jaar werken"?

No, that sounds unnatural in Dutch. Dutch sentences typically follow a strict "Time before Place" rule. The time when it happened (vorig jaar) needs to come before the place where it happened (in de fabriek).

If the subject was plural (they), what would the past tense of moeten be here?

If the subject were plural, like wij (we) or plural zij (they), the past tense would be moesten. For modal verbs in the past tense, you simply add -en to the singular form.