1926, since it's after 1920 it should also have the barrel code.
They month and year can be determined by the barrel code, all the details can be found on the Remington Society of America here:
http://remingtonsociety.com/rsa/questions/barrelcodes
Need the serial number to answer.
1931
1913
1919
1920
You cannot the serial number is required.
The serial number 4279990 is a partial serial number for this rifle. To determine the date the rifle was manufactured you need to provide a complete serial number that begins with letters.
Manufactured 1914
Manufactured 1909
Manufactured 1916
1920
In 1944 by Remington Rand