A woman and her daughter

Let the work rate of the woman and the daughter be $x$ and $y$ respectively. We know that

Work = Rate X Time

Let the amount of housework to be done be $w$ . We have:

$w=3x \implies$ Eq.(1)

$w=2(x+y) \implies$ Eq.(2)

Substitute Eq.(1) into Eq.(2):

$3x=2x+2y\implies x=2y\implies$ Eq.(3)

Now, let the time taken for the daughter to complete the housework be $t$ . We have

$w=yt$

Substitute Eq.(1) in here:

$3x=yt$

Substitute Eq.(3) in here:

$3(2y)=yt\\ 6y=yt\\ t=\boxed{6}$