Well, I thought I told you, but if you're really new and don't understand the terminology...
I the link I provided to the manual page for the mysqli_select_db() function, note the order of the two arguments (a.k.a. parameters) that are between the parentheses. The first one is the MySQLi connection or "link" object, the second one is the name of the database. Now look at your code:
$db_select = mysqli_select_db(DB_NAME,$this->conn);
You have them in the opposite order, so you just need to swap their order:
$db_select = mysqli_select_db($this->conn, DB_NAME);