Question 164392
Let x=number of quarts that needs to be drained and replaced with pure antifreeze
Now we know that the amount of pure antifreeze remaining after x amount has been drained (0.40(12-x)) plus the amount of pure antifreeze added (x) has to equal the amount of pure antifreeze in the final mixture (0.60*12).  So, our equation to solve is:

0.40(12-x)+x=0.60*12  get rid of parens (distributive law)
4.8-0.40x+x=7.2  subtract 4.8 from each side
4.8-4.8-0.40x+x=7.2-4.8  collect like terms
0.60x=2.4  divide each side by 0.60
x=4 quarts ----number of quarts that needs to be drained and replaced with pure antifreeze

CK
0.4*8+4=7.2
3.2+4=7.2
7.2=7.2

Hope this helps---ptaylor