This is the 7292nd most frequent Polish word.
kaczyńskiemu
"Kaczyńskiemu" is the dative singular form of "Kaczyński," meaning "to/for Kaczyński" in English.
In this sentence, 'Kaczyńskiemu' is in the dative case, denoting the indirect object of the verb, 'podarować' (to gift), meaning the action is directed toward Kaczyński.
„Podarowali książkę Kaczyńskiemu z dedykacją.
They gifted a book to Kaczyński with a dedication.
Here, 'Kaczyńskiemu' again appears in the dative case, indicating the person toward whom the sentiments (condolences) are expressed using the verb 'wyrazić' (to express).
„Wyrazili współczucie Kaczyńskiemu po stracie bliskiej osoby.
They expressed condolences to Kaczyński after the loss of a loved one.
In this usage, 'Kaczyńskiemu' serves as the dative form of the proper noun, illustrating the person receiving the advice given by the verb 'doradzić' (to advise).