Answer
$(-1,2)$ is not a solution of the inequality.
Work Step by Step
The given inequality is
$\Rightarrow 8x+y\gt -6$
Substitute $-1$ for $x$ and $2$ for $y$.
$\Rightarrow 8(-1)+2\gt -6$
Simplify.
$\Rightarrow -8+2\gt -6$
$\Rightarrow -6\gt -6$
False.
Hence, $(-1,2)$ is not a solution of the inequality.