Here's why:
* Pronoun: A pronoun replaces a noun. Examples include "he," "she," "it," "they," "them," "me," "you."
* Object Pronoun: An object pronoun is used as the object of a verb or preposition.
* Subject: In the sentence, "Green palm trees" is the subject, performing the action of growing.
* Preposition: "In" is a preposition.
* Object of Preposition: "The desert" is the object of the preposition "in."
Since there's no pronoun used as the object of the verb or preposition, there's no object pronoun in this sentence.