Should be as simple as
SELECT username, postnum FROM mybb_user ORDER BY postnum DESC LIMIT 1
or
SELECT username, count(username) as postCount FROM mybb_posts GROUP BY username ORDER BY postCount DESC limit 1
NOTE Do not use mysql* extension At very least use mysqli, but preferably PDO I am just showing it to you since that what you are using
$result = mysql_query('SELECT username, postnum FROM mybb_user ORDER BY postnum DESC LIMIT 1');
$row = mysql_fetch_assoc($result)
echo $row['username'] . $row['postnum'];