This is the 2234th most frequent Polish word.
rękę
"Rękę" means "hand" (accusative form) in English.
Here, 'rękę' (hand) is used in the context of greeting, specifically shaking hands.
On podał mi rękę na powitanie.
He extended his hand to greet me.
In this sentence, 'ręki' refers to a possessive form indicating the hand from which the book fell.
Podniosłem książkę, która wypadła z ręki.
I picked up the book that fell out of the hand.
The phrase 'o rękę' is a figurative expression meaning asking for permission to marry someone's daughter.