1. **State the problem:** We need to find the midpoint between two points on a coordinate plane, which represents the location of the carousel. 2. **Given points:** Ferris wheel at $(-5,4)$ and roller coaster entrance at $(6,-8)$. 3. **Midpoint formula:** The midpoint $M$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is calculated by $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right).$$ 4. **Apply the formula:** Substitute $x_1 = -5$, $y_1 = 4$, $x_2 = 6$, and $y_2 = -8$: $$M = \left(\frac{-5 + 6}{2}, \frac{4 + (-8)}{2}\right) = \left(\frac{1}{2}, \frac{-4}{2}\right).$$ 5. **Simplify:** $$M = \left(0.5, -2\right).$$ 6. **Conclusion:** The location of the carousel on the park's map is at coordinates $(0.5, -2)$.