For every 7 books purchased, Larry gets 2 free books. Larry purchased 21 books.
First, we find out how many sets of 7 books Larry purchased:
\[ \frac{21}{7} = 3 \]
Since Larry bought 3 sets of 7 books, he will get:
\[ 3 \times 2 = 6 \text{ free books} \]
Thus, Larry received 6 free books.