To determine the maximum number of pairs of soccer shorts Austin can buy, we first calculate how much money he has left after purchasing the soccer ball.
Austin has a total of $75 and he spends $12 on a soccer ball. The amount of money remaining after this purchase is:
\[ 75 - 12 = 63 \]
Now, Austin wants to spend the remaining $63 on soccer shorts, each of which costs $7. To find out how many pairs of soccer shorts he can buy, we divide the remaining money by the cost of one pair of shorts:
\[ \frac{63}{7} = 9 \]
Thus, the maximum number of pairs of soccer shorts Austin can buy is:
\[ \boxed{9} \]