Here we have some important part. We have to select a group of 6 which will be finally forming 2 groups with six children. Bu when we select a six group set the remain is also a six group set.
Ways to select 6 from 12 `= ^12c_6`
But when we select 6 from 12 the rest is also a group of six which is already included in the set we calculated. So to get the correct answers we have get the half of the `^12C_6` .
So ways to select 6 from 12 `= 1/2xx^12C_6 = 462`
So we have 462 ways to select groups of 6 children.