The inequality \( t > 9 \) indicates that the number of counselors needed at the summer camp must be greater than 9. Therefore, the solution of this inequality tells us that the number of counselors can be any integer greater than 9.
From the provided options, the correct interpretation based on the inequality \( t > 9 \) is:
The number of counselors can be 10, 11, or 12.
This is the only option that correctly reflects that the number of counselors must be greater than 9.