Question 6
The $2026$ FIFA World Cup consists of $48$ teams divided into $12$ groups of $4$ teams each. In every group, each team plays every other team exactly once. A win earns $3$ points, a draw earns $1$ point, and a loss earns $0$ points. After all group matches have been played, exactly $k$ teams finish with $6$ points. What is the largest possible value of $k$?