Today my english teacher insisted that the possessive adjective in the following sentence is THEIR pens! while I was trying to convince her that the correct answer is YOUR pens so which one of it is correct? the sentence goes like this:
Sara and you have pens. ________ pens are red.
Pronouns come in 3 persons: first, second, and third.
First-person pronouns refer to the speaker(s).
Second-person pronouns refer to the person or group being spoken to.
Third-person pronouns refer to a person or group that is not being spoken to.
If you are in the group being spoken about, a third-person pronoun cannot be used; the entire group inherits your "second-person-ness". If you are not in the group being spoken about, only one other person is available, so a third-person plural pronoun cannot be used. Therefore, "their" cannot be correct in this situation.
However, the sentence does allow for two possible pronouns, with 3 meanings:
1a: Sara and you have pens. Your pens are red.
The pens that you and Sara have are red. (This meaning would be conveyed by de-stressing "your" and stressing "pens" and "red"; the intent is to distinguish "pens that Sara and I have" from "pens that other people have.")1b: Sara and you have pens. Your pens are red.
Sara has pens, you have pens; Sara's pens are not red, your pens are red. (This meaning would be conveyed by stressing "Your" and "red"; the intent is to distinguish "pens that Sara has" from "pens that I have".)2: Sara and you have pens. Her pens are red.
Sara has pens, you have pens; Sara's pens are red, yours are not. The intent, again, is to distinguish "pens that Sara has" from "pens that I have".
If you have 1 pen and Sara has 1 pen, then option 1a above is the only valid choice; in option 1b and 2, the use of "pens" after the possessive pronoun requires more than one pen to belong to each person.
The usual order of the first sentence is "You and Sara have pens." But in any case, the second sentence must start with "your", not "their". Always.
Edited to add: I agree with the commenters that "Sara and you" is OK. But "you and Sara" is much more common, as this Google Ngram shows (with Sara replaced by John to get a reasonable hit count).
