Learn Dutch: Hebben jullie de goochelaar zien buigen? - Did you guys see the magician bow?

This is the core of the double infinitive rule! When a verb of perception like zien (to see) is used in the perfect tense along with another action verb like buigen (to bow), it drops its past participle form (gezien) and uses the full infinitive (zien) instead.

Why is the word order zien buigen and not buigen zien?

When you have a double infinitive at the end of a sentence, the verb of perception (zien) comes just before the action verb it is observing (buigen). They cluster together at the very end.

Why does the English translation say "Did you guys see" when the Dutch sentence uses the perfect tense Hebben ... zien?

In spoken Dutch, the present perfect is the most common way to talk about completed past events. English prefers the simple past ("Did you see"), but Dutch prefers the perfect tense, even though they describe the same past event.

I know jullie means "you" (plural). Does the verb hebben always go at the front here?

Yes, because this is a yes/no question. In Dutch yes/no questions, the conjugated verb (hebben) swaps places with the subject (jullie) and moves to the very beginning of the sentence.