What is Shashthī vibhakti

षष्ठी विभक्ति or Genitive Case of the noun-form represents the "whose" of the sentence.
In other words genitive case represents the genitive of the sentence.

Let us look at the following sentences to understand this.

Shashthī Vibhakti sentences in Sanskrit

1. रामस्य पुस्तकम् (Rama's book)
In this sentence, रामस्य is the genitive in the sentence.

2. नद्याः जलम् (Water of river)
In the above sentence, नद्याः is the genitive in the sentence.

In sentence 1 above, if we ask the question, 'whose book?' the answer that we get is 'Ram'.
In sentence 2 above, if we ask the question, 'whose water?' the answer that we get is 'River'.
So, in general, answer to the question 'whose' is the genitive of the sentence.

Examples of Shashthī Vibhakti in Sanskrit

Shashthī Vibhakti of Ram

विभक्ति	एकवचन	द्विवचन	बहुवचन
प्रथमा	रामस्य	रामयोः	रामाणाम्

Shashthī Vibhakti of Lataa

विभक्ति	एकवचन	द्विवचन	बहुवचन
प्रथमा	लतायाः	लतयोः	लतानाम्

Shashthī Vibhakti of Fal (Phal)

विभक्ति	एकवचन	द्विवचन	बहुवचन
प्रथमा	फलस्य	फलयोः	फलानाम्