We knew there were 82 at bats and an .8537 slugging %.
That gives us 70 bases. We knew the 18 bases from the doubles and the 3 bases from the triple. So that left 49 bases to find. A little hunting and pecking with numbers gives the 21 bases from singles and 28 from home runs as the only way to get to 49.
Just a quick guess on my part. But baseball stats are fun to play with.