Breakdown of Dziewczyna jest wdzięczna babci za prezent.
być
to be
babcia
the grandmother
prezent
gift
dziewczyna
the girl / the girlfriend
Questions & Answers about Dziewczyna jest wdzięczna babci za prezent.
Why is "grandmother" written as babci instead of babcia?
Because it is in the Dative case, which is used for the person receiving gratitude (answering "to whom?"). For feminine nouns ending in -cia like babcia, the Dative singular ending becomes -ci.
Why does the adjective wdzięczna end in -a?
The basic dictionary form is wdzięczny (grateful). It changes to the feminine form wdzięczna to match the subject of the sentence, dziewczyna (the girl).
Where is the word for "her" in this sentence?
In Polish, possessive pronouns like jej (her) or swojej (her own) are usually left out when it is obvious from the context whose grandmother it is. The sentence sounds more natural without it.
Why is it za prezent? What case does za take here?
When za is used to mean "for" (like thanking or being grateful for something), it requires the Accusative case. The word prezent is a masculine inanimate noun, so its Accusative form looks exactly the same as its basic dictionary form.