To find the midpoint of the segment with endpoints $(0, 8)$ and $(6, 4)$, we use the midpoint formula:

$\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Substituting the given coordinates into the formula:

$\text{Midpoint} = \left( \frac{0 + 6}{2}, \frac{8 + 4}{2} \right)$

Now, let's calculate:

$\text{Midpoint} = \left( \frac{6}{2}, \frac{12}{2} \right) = (3, 6)$

So, the midpoint of the segment is $(3, 6)$.

Would you like any further explanation or have any other questions?

Here are some related questions:

1. How do you find the equation of the line passing through two points?
2. What is the significance of the midpoint in coordinate geometry?
3. How do you find the area of a triangle given its vertices?
4. Can you determine the slope of a line using its endpoints?
5. How does the distance formula relate to the midpoint formula?

Tip: Always double-check your arithmetic when applying the midpoint formula, as small mistakes can lead to incorrect results.