6. (10 points) Four people, A, B, C, and D, took an exam. The combined score of A and B is 17 points higher than the combined score of C and D. A scored 4 points lower than B, and C scored 5 points higher than D. The highest score among the four is higher than the lowest score.

保留源文本的换行和格式如下：

6. (10 points) Four people, A, B, C, and D, took an exam.  
The combined score of A and B is 17 points higher than the combined score of C and D.  
A scored 4 points lower than B, and C scored 5 points higher than D.  
The highest score among the four is higher than the lowest score.
13
【Solution】Let's assume that person B scored $x$ points, then person A scored $x-4$ points, person C scored $y$ points, and person D scored $y-5$ points. Therefore, $(x+x-4)-(y+y-5)=17$,

Rearranging, we get: $2 x-2 y+1=17$,
So $2 x-2 y=16$,
So $x-y=8$,
Therefore, B scored higher than C;
Since $x-y=8$,
Then $(x-4)-(y-5)=9$,
So A scored higher than D,
Therefore, B scored the highest, and D scored the lowest,
So the difference between the highest and lowest scores among the four is:
$$
\begin{array}{l}
x-(y-5) \\
=x-y+5 \\
=8+5 \\
=13 \text { (points) }
\end{array}
$$

Answer: The highest score among the four is 13 points higher than the lowest score. Therefore, the answer is: 13.