1. **State the problem:** Solve the equation $$-3|6x - 4| = 54$$ for $$x$$. 2. **Isolate the absolute value:** Divide both sides by $$-3$$ to isolate $$|6x - 4|$$. $$-3|6x - 4| = 54$$ Dividing both sides by $$-3$$: $$\cancel{-3}|6x - 4| = \frac{54}{\cancel{-3}}$$ This simplifies to: $$|6x - 4| = -18$$ 3. **Analyze the absolute value:** The absolute value of any expression is always $$\geq 0$$, so it cannot equal a negative number. Since $$|6x - 4| = -18$$ has no solution, the original equation has **no solution**. **Final answer:** No solution