Answer
The ducks should fly at angle of $41.4^{\circ}$ south of west.
Work Step by Step
The relative velocity of the ducks with respect to the ground $v_{dg}$ is equal to the sum of the velocity of the ducks with respect to the air $v_{da}$ and the velocity of the air with respect to the ground $v_{ag}$.
The east-west component of $v_{dg}$ is zero. Let $\theta$ be the angle that is south of west that the ducks should fly. Therefore:
$v_{dg,x}= v_{da,x}+v_{ag,x} = 0$
$v_{da,x}= -v_{ag,x}$
$-(8.0~m/s)~cos(\theta) = -6.0~m/s$
$\theta = arccos(\frac{6.0}{8.0})$
$\theta = 41.4^{\circ}$
The ducks should fly at angle of $41.4^{\circ}$ south of west.
