Image doesn’t show for me. I would suggest it will be a case of changing the query to something like
$sql = "SELECT * FROM carbon_topics WHERE forum_catalog='news' ORDER BY id DESC LIMIT 20"; but without seeing the table layout it’s hard to say.
You also need to look at updating your database calls to PDO rather than the old-style mysql functions you are using, when your host upgrades to PHP 7 it will stop working.