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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:
\[
\boxed{9}
\]