This is the 5519th most frequent Polish word.
twojego
"Twojego" means "your" (singular, genitive case).
The word 'twojego' is used in this sentence as a possessive adjective. It is in accusative case, referring to the dog as the object of the verb 'widzę' (I see), showing possession belonging to 'you'.
Widzę twojego psa w parku.
I see your dog in the park.
Here, 'twojego' modifies 'brata' (brother), indicating possession ('your brother's'). This form is genitive, denoting that the book belongs to your brother.
Czy przyniosłeś książkę twojego brata?
Did you bring your brother's book?
In this example, 'twojego' is altered to 'twoim' to agree with the instrumental case required by the verb 'rozmawiać z,' referring to the ownership by 'you' and matching the masculine singular grammatical agreement.