You did not execute your query. So mysql_fetch_object() has nothing to return. Moreover, You need to connect to your database which is accomplished using mysql_connect(). To execute queries using mysql you can use mysql_query. Wrapping the previous notes in your code as an example would be:
// Connecting to database
$link = mysql_connect('localhost', 'mysql_user', 'mysql_password');
if (!$link) {
die('Could not connect: ' . mysql_error());
}
echo 'Connected successfully'; // Connected
$letter ='A';
$number = "SELECT number FROM progress";
$result = mysql_query($number); // Executing your query
$row = mysql_fetch_object($result); // Fetching your result into 'row'
$finalcode = $letter . $row;
In the above code, your object was fetched into $row. You can also specify the class name as the second parameter in mysql_fetch_object(), as an example:
$row = mysql_fetch_object($result,'foo');
Note: If your query is going to return more than one row you will have to loop over the $result, which has many examples in the manuals provided.
Note: Please have a look at mysqli overview, which should show you the differences between mysql and mysqli.