$delete_query holds hte result of your executed query, it's not a string. You have to make it a string, and execute it seperately if you want to print it.
$delete_query = "DELETE from EMPLOYEE WHERE EMPLOYEE.employeeid = '$employeeid'";
$result = mysql_query($delete_query) or die(mysql_error());
print $delete_query;
It really makes no difference if you use echo or print in this case.
But print returns true or false, which means you can use it in an if statement, whereas echo, if i'm not mistaken, doesn't.
Cgraz