Your code should look something like this:
$how_much = $this->wpdb->get_var("SELECT COUNT(*) FROM $this->table_name");
We don't need to use the prepare method, since this is not meant for table names, more here
And also... as you what are trying to do is going not in a good direction... I don't what to criticize you or anything... But I really suggest you to ask someone who knows better what WordPress can do, about what you need to do, and maybe he will suggest a better approach.
P.S: When you develop something, is good to enable the error/warnings/notices, and have a debugger, to know what's going on.