Check Remington Society of America here for date:
http://remingtonsociety.com/rsa/questions/barrelcodes
Depends on the model.
Remington Works - 1914 (late)
your Remington model 6 was made in 1998,due to the S prefix on the serial#.
1912
1920
1924
1912
1912
1923
1914
1911
1917