"I talk with your hamster."

Translation: Eu vorbesc cu hamsterul tău.

[itai_arbel]

please stop, you're making him uncomfortable.

[BrianDefferding]

I thought the "ul" suffix is definitive "the". Why does it apply here?

[MrtonPolgr]

Possessive is always considered definite in Romanian - you defined it by telling the possessor.