1. **State the problem:** Simplify the expression $3(u - 6) - 7u$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses. $$3(u - 6) - 7u = 3 \times u - 3 \times 6 - 7u = 3u - 18 - 7u$$ 3. **Combine like terms:** Combine the terms with $u$. $$3u - 7u - 18 = \cancel{3u} - \cancel{7u} - 18 = (3 - 7)u - 18 = -4u - 18$$ 4. **Final simplified expression:** $$\boxed{-4u - 18}$$ This means the original expression simplifies to $-4u - 18$.