This is the 435th most frequent German word.
euch
"euch" = "you" (plural, accusative or dative case).
In this sentence, 'euch' is used as the accusative form of the pronoun 'you' in its plural form, referring to multiple people being addressed directly as the recipients of the action.
Ich habe euch ein Geschenk gekauft.
I bought you all a gift.
Here, 'euch' functions as the dative plural pronoun for 'you', used to show the group of people that owns the dog.
Dieser Hund gehört nur euch.
This dog belongs only to you all.
In this example, 'euch' is in the accusative case, indicating the direct object (the group of people being seen).