1. The problem asks to find the number $x$ such that six times the difference of 11 and $x$ equals -72. 2. Write the equation: $6(11 - x) = -72$. 3. Distribute 6: $6 \times 11 - 6 \times x = 66 - 6x$. 4. So, $66 - 6x = -72$. 5. Subtract 66 from both sides: $$66 - 6x - 66 = -72 - 66$$ $$\cancel{66} - 6x - \cancel{66} = -72 - 66$$ $$-6x = -138$$ 6. Divide both sides by -6: $$\frac{-6x}{-6} = \frac{-138}{-6}$$ $$x = 23$$ 7. The solution is $x = 23$.