Is 'this" a possessive adjective?
No - it can be used as an adjective but not as a possessive one.
First, we need to know that a possessive adjective is 1. an adjective (that is, it modifies a noun) and 2. it demonstrates that the noun is owned or possessed by something or someone. For example, I can write:
The red luggage is my luggage. - "My" is a possessive adjective.
Does "this" meet that test? No - there isn't a way to use "this" as a possessive adjective. (The words in this list from the link below are possessive adjectives: my, your, his, her, its, our, your, their).
There is something else called a possessive pronoun - which is a pronoun that indicates possession. Here too, though, "this" doesn't meet the test:
The red luggage is mine - "mine" is a possessive pronoun. But the word "this" can't express the same feeling of ownership.
"This" can be both a pronoun (ex. This is mine) and an adjective (ex. I want this one, not that one) but not as a possessive form of them.