Four. (Total 20 points) On the 6 lines of the three edges of the tetrahedron $V-A B C$, what is the maximum number of pairs of lines that are perpendicular to each other? (Each pair consists of two lines)

保留源文本的换行和格式，翻译结果如下：

Four. (Total 20 points) On the 6 lines of the three edges of the tetrahedron $V-A B C$, what is the maximum number of pairs of lines that are perpendicular to each other? (Each pair consists of two lines)
Four, prove in three steps that there are at most 6 pairs of mutually perpendicular lines.
(1) 6 pairs can be achieved.
When $V A \perp$ plane $A B C$ and $A B \perp A C$, by the property of line perpendicular to a plane, we have $V A \perp A B, V A \perp B C, V A \perp C A$.
By the theorem of three perpendiculars, we also have $V C \perp A B, V B \perp A C$.

This results in 6 pairs of mutually perpendicular lines (refer to Figure 11).
(2) 8 pairs are impossible.
Since a triangle can have at most one right angle and at least two acute angles, 4 triangular faces must have at least 8 acute angles. Given that 6 lines can form $C_{0}^{2}=15$ pairs of lines, and $15-3=7$, we know that the number of mutually perpendicular lines does not exceed 7.
(3) 7 pairs are impossible.
If otherwise, there are 7 pairs of perpendicular lines, and since there are only 3 pairs of skew lines, at least 4 pairs of perpendicular lines must be coplanar, meaning all 4 faces of the tetrahedron must be right-angled triangles (yielding 4 pairs). Furthermore, the 3 pairs of skew lines must also be perpendicular. In this case, the projection of one vertex of the tetrahedron onto the opposite face must be the orthocenter of that triangle, and the orthocenter of a right-angled triangle is the right-angle vertex. Therefore, one lateral edge of the tetrahedron is perpendicular to the base, and the foot of the perpendicular is the vertex of the right-angled triangle (in Figure 11, $V A \perp$ plane $A B C$). At this point, the opposite face of the right-angle vertex of the base triangle is an acute triangle ($\triangle V B C$ is an acute triangle), which contradicts the fact that all 4 faces are right-angled triangles.
In summary, the maximum number of mutually perpendicular lines is 6.