Question

Let [n] = 1 if n is odd and 0 if n is even, for all positive integer n. if [n] * [n+8] = 0, then what is one possible value of n?

Answer 1

$[n][n+8]=0$

if either or both of $[n]$ and $[n+8]$ are 0, i.e. if one or both of $n$ and $n+8$ are even. But both will be even if $n$ is even, and odd otherwise, so any even $n$ will be a solution, e.g. $n=2$.