The exercise asks the reader to prove that $X$ is a finite covering (i.e., the number of points of $X$ lying over a given point of $L$ is finite and bounded) of $L$, where the affine varieties $X$ and $L$ are defined in the final part of exercise 5.16:
"...if $k$ is algebraically closed and $X$ is an affine algebraic variety in $k^n$ with coordinate ring $A\neq0$, then there exists a linear subspace $L$ of dimension $r$ in $k^n$ and a linear mapping of $k^n$ to $L$ which maps $X$ onto $L$."
Finally, the mapping $X\rightarrow L$ is given by the linear relation between the $x$'s and $y$'s when we are trying to prove the Noether normalization theorem in the first part of exercise 5.16.
Maybe that's really easy, but I have no idea.