What is a board game in which players try to transfer their pieces from own opponents bases?

You're likely thinking of a game like Checkers or Draughts.

Here's how they work:

* Objective: The goal is to capture all of your opponent's pieces and/or to block them from moving.

* Movement: Pieces move diagonally across the board, capturing opponent's pieces by jumping over them.

* Kinging: In some versions, when a piece reaches the opposite side of the board, it becomes a "king" with special movement abilities.

Other similar games:

* Chinese Checkers: Players move their pieces around a star-shaped board, aiming to be the first to get all their pieces into their opponent's starting area.

* Halma: Players move their pieces across the board, trying to be the first to get all their pieces into their opponent's starting area.

Let me know if you'd like to know more about any of these games!