Learn Dutch: Zouden jullie de afspraak annuleren? - Would you cancel the appointment?

Zouden is the plural form. Because the subject is jullie (you, plural), the verb must be plural too. If you were asking just one person informally, it would be Zou jij de afspraak annuleren?.

Why is the verb annuleren at the very end of the sentence?

In Dutch, when you have an auxiliary (helping) verb like zouden, the main verb in its full infinitive form (annuleren) gets pushed to the very end of the clause. This is the standard Dutch word order whenever a sentence has two verbs.

Is this sentence a polite request to cancel, or a hypothetical question?

As written, it sounds more like a hypothetical question: "Would you cancel the appointment? (If you were in my shoes)." If you want to use zouden to make a polite request, the Dutch usually soften it by adding a filler word like even or misschien. For example: Zouden jullie misschien de afspraak annuleren?.

Is there a more common, everyday word for canceling an appointment?

Yes, annuleren is quite formal. In everyday speech, Dutch people often use afzeggen (a separable verb meaning to call off). A native speaker might instead say: Zouden jullie de afspraak afzeggen?.