The correct answer is: [B]: "through a beautiful courtyard" .
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Note: A 'prepositional phrase' must start with a preposition; and in addition to including the preposition; the 'prepositional phrase must include its object as well.
So, "Choice [A]: "enter through" ; is clearly incorrect, since it does not start with a preposition. Furthermore, there is no object.
Consider: "Choice: [C]: "through a beautiful" . This choice is incorrect; since there is no object; so this choice is incorrect because it is "incomplete" for the purpose of meeting the criteria for a "prepositional phrase.
Choice: [B]: "through a beautiful courtyard" ; is correct; since this is modifying phrase that: 1) begins with a preposition—"through" ; and includes its object—"courtyard"—and as such, meets the criteria for a "prepositional phrase".
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