6. There are 9 points on a circle, and 3 triangles are formed using these 9 points as vertices. When these 3 triangles have no common vertices and their sides do not intersect, we call it a configuration. The number of configurations that satisfy this condition is ( ).
(A) 3
(B) 6
(C) 9
(D) 12
6.D.

Let these 9 points be denoted as $A_{1}, A_{2}, \cdots, A_{9}$. We consider two cases:
(1) When the 9 points are divided into 3 groups, with each adjacent 3 points forming a triangle (as shown in Figure 5), then these 3 triangles have no common points and their sides do not intersect. Since there are only 3 ways to group the points like this, there are a total of 3 configurations.
(2) When any 2 adjacent points are chosen from the 9 points, and then the points 3 positions to the left and right of these 2 points are connected to the opposite vertex, these 3 points form a triangle, and the 3 points on the same side form another triangle (as shown in Figure 6). Then these 3 triangles have no common vertices and their sides do not intersect. Since there are 9 ways to choose 2 adjacent points from the 9 points, there are a total of 9 configurations.
Combining (1) and (2), there are a total of 12 configurations.