1. **Problem:** Find the slope between points $(-2, 3)$ and $(6, 5)$. 2. **Formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Apply the formula:** $$m = \frac{5 - 3}{6 - (-2)} = \frac{2}{6 + 2} = \frac{2}{8}$$ 4. **Simplify the fraction:** $$m = \frac{\cancel{2}^1}{\cancel{8}^4} = \frac{1}{4}$$ 5. **Answer:** The slope between the points $(-2, 3)$ and $(6, 5)$ is $\boxed{\frac{1}{4}}$.