In Khitan, each player wants to eliminate the opponent's pieces – but both players start with the same number of (nearly) identical pieces, so you'll need to play carefully in order not to get knocked down yourself.
To set up, each player takes a set of hexagonal pieces, which are double-sided and have the same six colors on their two faces, and places them in the starting locations on the board. On a turn, you flip one of your pieces to an adjacent space. If a colored edge on that piece is now in line with an identically colored edge on an opponent's piece, remove the opponent's piece from the board. More that one piece can be destroyed with the same move. Zap all the opponent's pieces, and you win!
Khitan includes two variants. In the first, each player has a reserve of three pieces, and the first three times that you eliminate an opponent's piece, you add a new piece to your side of the board. (NB: You can't make captures when placing a piece, only when flipping.) In the second variant, each player has a reserve of six pieces and this reserve is replenished by pieces removed from the board, so you'll need to set up multiple attacks to keep the opponent from playing tit-for-tat and staying alive forever.