As I understand it, shifted output means first getting the output and then shifting it. We feed in $x[n]$, and get our output as $x[2n]$. Then we shift it by $k$ to get $x[2n-k]$. This is the shifted output.
Now, for output of the shifted input, we shift the input to get $x[n-k]$, then feed it as input to get output as $x[2(n-k)]=x[2n-2k]$
However, the text in the image has these answers reversed. Is there something I'm not getting?