What board game played with counters and throw sticks is called?

The board game you are referring to is likely "Pachisi." It is a traditional Indian game that involves players moving their pieces around a cross-shaped board based on the roll of cowrie shells or the throw of sticks. The objective is to move all your pieces to the home area before your opponents. Variants of Pachisi have influenced many modern Board Games, including Ludo and Parcheesi.