1. **State the problem:** Solve the equation $6(x+18)=192$ for $x$. 2. **Use the distributive property:** Multiply 6 by each term inside the parentheses. $$6(x+18) = 6 \times x + 6 \times 18 = 6x + 108$$ 3. **Rewrite the equation:** $$6x + 108 = 192$$ 4. **Isolate the term with $x$:** Subtract 108 from both sides. $$6x + \cancel{108} - \cancel{108} = 192 - 108$$ $$6x = 84$$ 5. **Solve for $x$:** Divide both sides by 6. $$\frac{6x}{\cancel{6}} = \frac{84}{\cancel{6}}$$ $$x = 14$$ 6. **Final answer:** $$\boxed{14}$$