1. **State the problem:** We are given two similar triangles $\triangle CGR \sim \triangle SDA$ with side lengths expressed as $AD = -2x - 8$, $GR = 6$, $CR = 12$, and $AS = -3x - 6$. We need to write an equation relating the side lengths and solve for $x$. 2. **Write the proportion from similarity:** Since the triangles are similar, corresponding sides are proportional. The problem gives the proportion: $$\frac{-2x - 8}{6} = \frac{-3x - 6}{12}$$ 3. **Solve the equation:** Cross-multiply to eliminate denominators: $$12(-2x - 8) = 6(-3x - 6)$$ 4. **Distribute:** $$-24x - 96 = -18x - 36$$ 5. **Bring all terms involving $x$ to one side and constants to the other:** $$-24x + 18x = -36 + 96$$ 6. **Simplify:** $$-6x = 60$$ 7. **Divide both sides by $-6$:** $$x = \frac{60}{\cancel{-6}}\cancel{-1} = -10$$ 8. **Final answer:** $$x = -10.00$$