1. **State the problem:** Solve the equation $$-2(x + 3) = 6x + 8$$ for $x$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses. $$-2 \times x = -2x$$ $$-2 \times 3 = -6$$ So the equation becomes: $$-2x - 6 = 6x + 8$$ 3. **Collect like terms:** Add $2x$ to both sides to move all $x$ terms to the right. $$\cancel{-2x} - 6 + 2x = 6x + 8 + 2x$$ Simplifies to: $$-6 = 8x + 8$$ 4. **Isolate the variable term:** Subtract $8$ from both sides. $$-6 - 8 = 8x + \cancel{8} - 8$$ Simplifies to: $$-14 = 8x$$ 5. **Solve for $x$:** Divide both sides by $8$. $$\frac{-14}{\cancel{8}} = \frac{8x}{\cancel{8}}$$ Simplifies to: $$x = -\frac{14}{8}$$ 6. **Simplify the fraction:** Both numerator and denominator can be divided by $2$. $$x = -\frac{14 \div 2}{8 \div 2} = -\frac{7}{4}$$ **Final answer:** $$x = -\frac{7}{4}$$ Among the options, $x = -\frac{14}{8}$ corresponds to option D, which is equivalent to $-\frac{7}{4}$ after simplification.