6. 6 There are 25 football teams participating in a round-robin tournament. After the tournament, it was found that the total number of goals scored in each match and the total number of goals scored by each team did not exceed 4. It is known that Team A scored the most total goals compared to any other team, and conceded the fewest total goals compared to any other team. What is the worst rank that Team A can achieve?
[Solution] Team $A$ could be the last place.
Let the other 24 teams be $B_{1}, B_{2}, \cdots, B_{24}$, and divide the 25 teams into 8 groups, where the first group is $\left\{A, B_{1}, B_{2}, B_{3}\right\}$, and the other 7 groups each have 3 teams.

Assume the match results in the first group are: $A$ beats $B_{1}: 4: 0, A$ loses to $B_{2}: 0: 1, A$ loses to $B_{3}: 0: 1, B_{1}$ beats $B_{2}: 1: 0, B_{1}$ beats $B_{3}: 1: 0, B_{2}$ draws with $B_{3}: 2: 2$. In the other 7 groups, each of the 3 teams wins 1 match and loses 1 match. The score for each match is $2: 1$, and the result of any match between teams from different groups is $0: 0$. This way, Team $A$ has 1 win, 2 losses, and 21 draws, scoring 23 points (the football scoring rule is 2 points for a win, 1 point for a draw, and 0 points for a loss), Team $B_{1}$ has 2 wins, 1 loss, and 21 draws, scoring 25 points, Teams $B_{2}$ and $B_{3}$ each have 1 win, 1 loss, and 22 draws, scoring 24 points each. The other 21 teams in the 7 groups each have 1 win, 1 loss, and 22 draws, scoring 24 points each. It is clear that Team $A$ is the last place.

Moreover, Team $A$ scores 4 goals and concedes 2; Team $B_{1}$ scores 2 goals and concedes 4; Teams $B_{2}$ and $B_{3}$ each score 3 goals and concede 3; Teams $B_{4}, B_{5}, \cdots, B_{24}$ also each score 3 goals and concede 3. It is clear that Team $A$ scores more goals than any other team and concedes fewer goals than any other team. Therefore, the above match results meet the requirements of the problem.