No, the word 'your' is a possessive adjective, a type of pronoun. The word 'letters' is a plural noun.
The term 'your letters' is a nounphrase, any word or group of words based on a noun or pronoun (without a verb) that can function in a sentence as a subject, object of a verb or a preposition. The noun phrase 'your letters' is based on the noun 'letters'.
EXAMPLES
noun phrase as subject: Your letters are always so cheerful.
noun phrase as object: I keep your letters in a fancy box.
No, he is not possessive. The possessive form would be his.
The possessive noun of Sam is Sam's.
The possessive noun for "diplomat" is "diplomat's." For example: The diplomat's speech was well-received.
No, "she's" stands for she is. The singular possessive noun for a female is her or hers.
The possessive form for the plural noun wives is wives'.
It only becomes a plural possessive noun when you add extra letters - e.g. princesses'
The possessive singular noun is explorer's. The possessive plural noun is explorers'.
The possessive form for the noun coyote is coyote's.
The possessive form of zoo is zoo's.
The possessive form for the noun preacher is preacher's.
The possessive form for the noun laboratory is laboratory's.
No, he is not possessive. The possessive form would be his.
The possessive form for the noun oxygen is oxygen's.
The possessive form is grandson's.
The possessive form is island's.
The possessive form for the noun coyote is coyote's.
The possessive noun of Sam is Sam's.