I am simplifying the following equation.
$$ =\sum_{k=-\infty}^{\infty}{ x_k \sum_{n=-\infty}^{\infty}{h_{n-k}}}$$
If sum index for $n$ is changed to $r=n-k$, where $n = r+k$.
$$ =\sum_{k=-\infty}^{\infty}x_k \sum_{r=-\infty-k}^{\infty-k}{h_r}$$
Question: $\Rightarrow$ is it valid to change the index of the second summation as follows: $$\{-\infty-k \rightarrow -\infty\} \text{ and } \{\infty-k \rightarrow \infty\}$$
$$ = \sum_{k=-\infty}^{\infty}{ x_k \sum_{r=-\infty}^{\infty}{h_r}}$$