A soccer game ends with the final score 6:4 How many scores were possible at half time

Let's denote the score at half time as A:B. Since the final score was 6:4, this means that team 1 scored 6 goals in total and team 2 scored 4 goals in total.

At half time, the total number of goals scored is A + B.
We know that A + B must be less than or equal to 6 (since team 1 scored 6 goals in total) and less than or equal to 4 (since team 2 scored 4 goals in total).

The possible scores at half time can be:
1. A = 0, B = 0
2. A = 1, B = 0
3. A = 1, B = 1
4. A = 2, B = 0
5. A = 2, B = 1
6. A = 3, B = 0
7. A = 3, B = 1
8. A = 4, B = 0
9. A = 4, B = 1
10. A = 5, B = 0
11. A = 5, B = 1
12. A = 6, B = 0

Therefore, there are 12 possible scores at half time.

\boxed{12} possible scores at half time.