Identify the determiner from the sentence below: "We met some interesting people in our hotel when we were on holiday."

The right answer will be: Our. It is a possessive determiner. 

Determiners are words such as the, my, this, some, twenty, each, any, which are used before nouns. 

Determiners include the following common types:

- Articles: a/an, the

- Demonstratives: this, that, these, those

- Possessives: my, your, his, her, its, our, their, x’s (possessive ’s)

- Quantifiers: (a) few, fewer, (a) little, many, much, more, most, some, any, etc.

Source: Cambridge Dictionary Grammar reference.