This is the 606th most frequent Serbian word.
његовом
"Његовом" means "his" (dative or instrumental case) in English.
In this sentence, 'његовом' is the dative form of 'његов', used to refer to 'his' as it relates to 'effort' in its dative case, indicating direction or reference.
Његовом напору се дивимо.
We admire his effort.
Here, 'његовом' is the locative form of 'његов', used to describe possession ('his') associated with 'success' in its locative case, since it follows the preposition 'о' ('about').
Говорили су о његовом успеху.
They spoke about his success.
In this context, 'његовом' is the dative form of 'његов', linked to 'brother' in dative case, as an indirect object of 'offered.'