Final answer:
The pronouns in the sentence are 'their' and 'our,' which are both possessive pronouns.
Step-by-step explanation:
In the sentence, "Gus and Elena and their two children are coming to our house for a barbeque," the pronouns are "their" and "our." "Their" is a possessive pronoun indicating that something belongs to Gus, Elena, and their children.
In this case, it shows that the two children belong to Gus and Elena. "Our" is also a possessive pronoun, indicating something belongs to the speaker and at least one other person; in this context, it is the house that is shared.