Read the Constitutional amendment: no soldier shall, what does this amendment prevent the US government from doing?

No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law.

this prevents the US government from intruding on someone's private property

affirmative action refers to the policies that take gender, race, or ethnicity into account in order to promote equal opportunity.

employers subject to title vii are prohibited from taking race or sex into account in any employment decisions. aa is a penalty for having any job group substantially statistically "underutilized" in any race or either sex. the employer must take steps to eliminate the underutilization, then stop, ending its aa efforts