With is a preposition.

Is with a prepositional phrase?

At a minimum, a prepositional phrase consists of one preposition and the object it governs. … Some of the most common prepositions that begin prepositional phrases are to, of, about, at, before, after, by, behind, during, for, from, in, over, under, and with.

What type of grammar is these?

This and these are demonstratives, which means they indicate a specific noun in a sentence. The two words are similar because they refer to nouns that are near in space and time. This is used with singular or uncountable nouns (i.e. this egg or this music). These refers to plural nouns (i.e. these cookies).