How old Remington model -4 -22 cal?

They were made from 1890 to 1933, if it was made after 1920 (serial after 267K or so) there will be a barrel date code stamp on it. Check the Remington Society of America for a diagram and details. http://remingtonsociety.com/rsa/questions/barrelcodes

I can date some back to 1905 based on serial before that is a mystery ;) End of 1905 was 163884.