Shouldn't this translate to "¿Queréis que Juan recitar un poema?"? However, in a kwiz, "¿Queréis que Juan recite un poema?", was the correct answer. But 'to recite' is in the infinitive.
When you want someone else to do something, the verb is conjugated in the subjunctive so recitar changes to recite.
Here is a Kwiziq lesson that explains this. Have a look here.
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