What is the sum of all positive integers $t$ such that $1.2t \leq 9.6$?
Dividing both sides of the inequality by 1.2, we have $t \le \dfrac{9.6}{1.2}$. The right side of this inequality is equal to $\dfrac{96}{12}$, which is $8$.

Thus, we are looking for the sum of all positive integers less than or equal to $8$. This is $1+2+3+4+5+6+7+8 = \boxed{36}$.