To solve the equation \( 5m - 2m + 6m = -81 \), first combine the like terms on the left side:
\[ (5m - 2m + 6m) = (5 - 2 + 6)m = 9m \]
Next, the equation simplifies to:
\[ 9m = -81 \]
Now, divide both sides by 9 to solve for \( m \):
\[ m = \frac{-81}{9} = -9 \]
Thus, the solution is:
\[ \boxed{-9} \]