#### Answer

2 liters of the 20% dye solution.
4 liters of the 40% dye solution.

#### Work Step by Step

number of liters$\times$dye solution strength=amount of dye solution
x=# of liters
Liters of 20% solution = x
Liters of 50% solution = 6-x
Liters of 40% solution needed = 6
$0.20x + 0.50(6-x)=0.40(6)$
$0.20x + 3 - 0.50x=2.4$
$-0.30x+3=2.4$
$-0.30x=2.4-3$
$-0.30x=-0.6$
$x=-0.6\div-0.30$
$x=2$ so we need 2 liters of the 20% solution
50% solution = 6-x with x=2
50% solution =6-2=4 so we'll need 4 liters of the 50% solution.