Answer
$-6$ is not a solution.
Work Step by Step
Substitute $-6$ to $m$ to obtain:
$\begin{align*}
10&\le3-m\\
10&\le3-(-6)\\
10&\le3+6\\
10&\le9
\end{align*}$
The resulting statement above is false therefore $-6$ is NOT a solution of the given inequality.