Answer
Please see the figure attached.
Work Step by Step
The contour map of $f\left( {x,y} \right) = {x^2} + {y^2}$ with level curves $c = 0,4,8,12,16$ is obtained by plotting the curves:
$c = {x^2} + {y^2}$, ${\ \ \ }$ for $c = 0,4,8,12,16$
Notice that these are circles of radius $\sqrt c $ centered at $\left( {0,0} \right)$.
