This is the 13995th most frequent Russian word.
объявлению
"Announcement" or "advertisement."
In this sentence, "объявлению" is used in the dative case as it reflects the indirect object of the response action.
Я ответил на объявлению о продаже дома.
I responded to the advertisement for the house sale.
Here, "объявление" is in the nominative case acting as the subject of the verb "опубликовала."
Газета опубликовала новое объявление о работе.
The newspaper published a new job announcement.
In this sentence, "объявление" is in the accusative case as the direct object of the verb "видели."