This is the 4246th most frequent German word.
deinem
"Deinem" means "your" (possessive, referring to a singular informal 'you' in the dative case).
'deinem' is the dative form of 'dein', signifying 'your' in relation to 'Hund', which requires dative due to the verb 'geben'.
Ich habe deinem Hund gestern das Spielzeug gegeben.
I gave your dog the toy yesterday.
'deinem' is used here in the dative case because the verb 'helfen' requires the object (Bruder) to be in the dative case.
Ich helfe deinem Bruder bei den Hausaufgaben.
I help your brother with the homework.
'deinem' is in dative case due to the preposition 'zu', which requires a dative object ('Fest').