You can say "Debes recoger tu cuarto" or "Debes ordenar tu habitación". Both are correct; recoger and ordenar are synonyms and the same goes for cuarto and habitación.
But note that your sentence is saying "Debes ordenar su cuarto"; you must match the conjugation with the possessive. The correct possessive here should be "tu", not "su", as you are using the you informal conjugation. If you want to make this sentence more formal you could also say "(Usted) debe ordenar su cuarto."
Gracias y saludos
Thank you Inma for your clear explanation. I get it now.
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