KöMaL 2019 C1538

Six pairs of twin brothers participated in one of the practices of the Twins' Table Tennis Club. The coaches did not want any brothers to play at the same table. $a)$ In how many different ways may they divide the players to play round-the-table games at two different tables? $b)$ In how many different ways is it possible to divide the players into sets of four to play doubles at three different tables? (The position of the players at the tables does not matter.)