1. **State the problem:** Solve for $x$ in the equation $$2(x-6) = 3(2x + 14)$$. 2. **Use the distributive property:** Multiply out the parentheses. $$2 \times (x-6) = 2x - 12$$ $$3 \times (2x + 14) = 6x + 42$$ So the equation becomes: $$2x - 12 = 6x + 42$$ 3. **Isolate the variable terms:** Move all terms involving $x$ to one side and constants to the other. Subtract $2x$ from both sides: $$-12 = 6x - 2x + 42$$ $$-12 = 4x + 42$$ 4. **Isolate $x$:** Subtract 42 from both sides: $$-12 - 42 = 4x$$ $$-54 = 4x$$ 5. **Solve for $x$:** Divide both sides by 4: $$x = \frac{-54}{4} = -\frac{27}{2} = -13.5$$ **Final answer:** $$x = -13.5$$