1. **State the problem:** Solve the equation $Y - (-6) = -\frac{6}{8}(X - (-2))$ for $Y$ in terms of $X$. 2. **Rewrite the equation:** The equation is $Y + 6 = -\frac{6}{8}(X + 2)$. 3. **Simplify the fraction:** $-\frac{6}{8} = -\frac{3}{4}$, so the equation becomes $Y + 6 = -\frac{3}{4}(X + 2)$. 4. **Distribute the fraction:** $Y + 6 = -\frac{3}{4}X - \frac{3}{4} \times 2 = -\frac{3}{4}X - \frac{3}{2}$. 5. **Isolate $Y$:** Subtract 6 from both sides: $$Y = -\frac{3}{4}X - \frac{3}{2} - 6$$ 6. **Combine constants:** Convert 6 to $\frac{12}{2}$ to combine with $-\frac{3}{2}$: $$Y = -\frac{3}{4}X - \frac{3}{2} - \frac{12}{2} = -\frac{3}{4}X - \frac{15}{2}$$ **Final answer:** $$Y = -\frac{3}{4}X - \frac{15}{2}$$