Question 654847
it's:

{{{12!/6!6!}}}


={{{(12*11*10*9*8*7*6*5*4*3*2*1)/(6*5*4*3*2*1*6*5*4*3*2*1)}}}


={{{(12*11*10*9*8*7*cross(6*5*4*3*2*1))/(cross(6*5*4*3*2*1)*6*5*4*3*2*1)}}}


={{{(cross(12)2*11*cross(10)2*cross(9)3*cross(8)2*7)/(cross(6)*cross(5)*cross(4)*cross(3)*2*1)}}}


={{{(cross(2)*11*2*3*2*7)/(cross(2)*1)}}}


={{{11*2*3*2*7}}}


={{{924}}}


Here's why:

There are {{{12}}}! unique ways the {{{12}}} children can be arranged. 

Since we don't care about the order of the {{{6}}} boys, we divide by the number of ways {{{6}}} boys can be arranged, or {{{6}}}!. 

Similarly we don't care how the girls are arranged, so we divide again by {{{6}}}!. 

That leaves the number of ways {{{12}}} children consisting of {{{6}}}boys and {{{6}}} girls can be arranged if you all you care about is gender.