Official solution
\[{C_1}{\rm{ }}:{\rm{ }}\left| {y{\rm{ }}-{\rm{ }}x} \right|{\rm{ }} \le {\rm{ }}2\]
\[{C_2}{\rm{ }}:{\rm{ }}\left| {y{\rm{ + }}x} \right|{\rm{ }} \le {\rm{ }}2\]
Now region is square
shown figure is square with side length 2\[\sqrt 2\] .