Answer
$(m-3n)(m+9n)$
Work Step by Step
List the pairs of factors of $-27$. Identify the pair that has a sum of $6$.
$\left[\begin{array}{lll}
\text{Factors of -27 } & \text{Sum of factors} & \\
1\text{ and }-27 & -26 & \\
-1\text{ and }27 & 26 & \\
3\text{ and }-9 & -6 & \\
-3\text{ and }9 & 6 & \text{...is what we need}
\end{array}\right]$
$m^{2}+6mn-27n^{2}=(m-3n)(m+9n)$
