This is the 4905th most frequent Russian word.
кварталу
The Russian word "кварталу" is the dative singular form of "квартал," meaning "quarter" (as in a city block, a financial quarter, or a three-month period).
Here 'кварталу' is in the dative case, implying the area of the city where the walking occurs.
Мы гуляли по старому кварталу города.
We walked around the old quarter of the city.
In this instance, 'кварталу' is in the dative case, indicating the time frame (quarter) by which the completion occurs.
Ремонт дома завершится к следующему кварталу.
The house renovations will be finished by the next quarter.
Here 'кварталу' again is in the dative case but it's used flexibly to imply a situational focus regarding the area under discussion.