I assume if it had a model you would have mentioned it so I suspect your talking about a model 12. Manufactured in 1919.
RW is Remington Works, not part of the serial no. 1912.
It is a Remington Model 12 .22 cal. pump
Made 1915
1920
1913
1913
Made in 1908
Early 1909
With that type of serial number Tue gun can't be that old. Probably 50
100-500 USD
If it's not marked it's a model 12 made in 1914.
Hexagon barrel what? Model? pump, rolling block, ?? Condition?