Update one mysql column when another is edited
The code doesn't look like valid Mysql code:


ALTER is not a valid option
No AS in Mysql
IF UPDATE(column) 


UPDATE(column) tests whether column updated in SQLServer, not in Mysql
IF syntax is invalid (check https://dev.mysql.com/doc/refman/5.5/en/if.html) 

Finally, you can change value of the record which is being modified in BEFORE trigger, not in AFTER.  


You need something like 

drop trigger if exists last_progress_date;
delimiter // 
CREATE TRIGGER last_progress_date BEFORE UPDATE ON wp_task_mgr 
FOR EACH ROW     
BEGIN
   --assuming progress_percentage is not nullable; if it is, the condition 
   -- needs to be modified to properly handle NULL values
   IF (NEW.progress_percentage != OLD.progress_percentage) 
   THEN
       SET NEW.last_progress_date = GETDATE();
   END IF;
END;
//
DELIMITER ;