problem with sql query

Your code should look something like this:

 $this->table_name="table_name";

    $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.