1. **State the problem:** We need to solve the system of equations graphically: $$y = x + 4$$ $$y = -\frac{3}{2}x - 6$$ 2. **Recall the method:** The solution to the system is the point(s) where the two lines intersect. 3. **Set the equations equal to find the intersection:** $$x + 4 = -\frac{3}{2}x - 6$$ 4. **Solve for $x$:** Add $\frac{3}{2}x$ to both sides: $$x + \frac{3}{2}x + 4 = -6$$ Combine like terms: $$\left(1 + \frac{3}{2}\right)x + 4 = -6$$ $$\frac{2}{2}x + \frac{3}{2}x + 4 = -6$$ $$\frac{5}{2}x + 4 = -6$$ Subtract 4 from both sides: $$\frac{5}{2}x + \cancel{4} - 4 = -6 - 4$$ $$\frac{5}{2}x = -10$$ Divide both sides by $\frac{5}{2}$: $$x = \frac{-10}{\cancel{\frac{5}{2}}} \times \cancel{\frac{2}{5}} = -10 \times \frac{2}{5} = -4$$ 5. **Find $y$ by substituting $x = -4$ into one of the original equations:** Using $y = x + 4$: $$y = -4 + 4 = 0$$ 6. **Conclusion:** The lines intersect at the point $$\boxed{(-4, 0)}$$. This is the graphical solution to the system.