6. (10 points) There are 12 students playing a card game, with 4 participants each time, and any 2 students can participate together at most 1 time. How many times can they play $\qquad$ at most.
【Analysis】First, analyze that the students can be labeled, and then enumerate.
【Solution】According to the problem, we know:
Number the students from 1 to 12.
If the groups are 1-4, 5-8, and 9-12, the next group will not meet the requirements, so we need to form as many groups as possible.

The first group is $1,2,3,4$.
The second group is $1,5,6,7$.
The third group is $2,5,8,9$.
The fourth group is $3,6,8,10$.
The fifth group is $4,5,8,11$.
The sixth group is $3,5,9,10$.
The seventh group is $4,6,9,11$.
The eighth group is $1,7,9,12$.
The ninth group is $2,6,10,12$.
Therefore, the answer is: 9