The :new.column_name syntax only applies to the table that the trigger is on. You will need to use an update statement on the other table.
CREATE OR REPLACE TRIGGER auto_notify
BEFORE UPDATE OF result ON sample_result
FOR EACH ROW
WHEN (NEW.PROPERTYID = 'Action Taken')
SET samplenotify = 'S'
WHERE sampleid = :NEW.sampleid;
Thank you BarbaraBoehmer.
A little twist from guidance from you has solved my problem.
Thanks a lot