Answer
The star is moving at a speed of $682~km/s$ with respect to the Earth. Since the observed wavelength is longer than the emitted wavelength, the star must be moving away from the Earth.
Work Step by Step
Let $\lambda_0 = 659.6~nm$ and let $\lambda' = 661.1~nm$
We can find the speed of the star $v$ with respect to the Earth:
$\frac{v}{c} = \frac{\lambda'-\lambda_0}{\lambda_0}$
$v = \frac{\lambda'-\lambda_0}{\lambda_0}~c$
$v = \frac{661.1~nm-659.6~nm}{659.6~nm}~(3.0\times 10^8~m/s)$
$v = 6.82\times 10^5~m/s$
$v = 682~km/s$
The star is moving at a speed of $682~km/s$ with respect to the Earth. Since the observed wavelength is longer than the emitted wavelength, the star must be moving away from the Earth.
