1. **State the problem:** We need to find the horizontal distance between points A and B on the coordinate plane. 2. **Identify the coordinates:** Point A is at $(0,4)$ and point B is at $(2,4)$. 3. **Recall the formula for horizontal distance:** The horizontal distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the absolute difference of their $x$-coordinates: $$\text{Horizontal distance} = |x_2 - x_1|$$ 4. **Apply the formula:** $$|2 - 0| = 2$$ 5. **Interpretation:** The horizontal distance between points A and B is 2 units. **Final answer:** 2 units