Thinking outloud here...
If the mean from 11 games was 6, then she scored a total of 66 points in the 11 games.
If the mode was 8, then she scored 8 more than any other score, so let's say she scored 8 in three games. (That's 24 points scored)
If the median was 7, then when the scores are lined up in order, 7 will be the middle score and we have at least 31 points scored. We need 35 more points.
So far we have:
__, __, __, __, __, 7, 8, 8, 8, __, __
Let's add some low scores:
3, 4, 5, 5, 5, 7, 8, 8, 8, __, __
That added 22 points to the total, meaning we need 13 more. We can't do that with scores higher than 8.
So, let's add in two scores of 9 and see what we need to take away from the other side:
3, 4, 5, 5, 5, 7, 8, 8, 8, 9, 9
This gives us 71, so we're 5 points over 66. Let's knock down the lower scores each by 1.
2, 3, 4, 4, 4, 7, 8, 8, 8, 9, 9
That's 66 points, 11 games, a mean of 6, a mode of 8, and a median of 7.
There ya go.
