serial #
1947
You can't. You can find the serial number and from that you can get a ballpark figure on date of manufacturer
Go to Browning's site, Support, Date Your Shotgun.
You must call Browning with the serial number to find out.
"Ithaca Featherlight Repeaters" by Walter Claude Snyder
By the serial #
Go to Browning.com to date it. For the Grade, you will either have to provide a detailed description or get a book on Brownings.
Date code stamp on barrel if 1921 or later, before that serial no. See related links for date code info.
Your question cannot be answered without you providing the name of the maker of your shotgun,and then we can determine if there is any public data to identify the year of manufacture.
I have a partial answer and plan to submit a question. Ithaca hammer shotguns with serial #'s below 33011 were produced before 1899. I have a hammer double barrel stagecoach shotgun with serial # 15864. I will post a question to find out its age.
Unlikely that detailed sn data has been published.
The serial of you Parker shotgun did not print in your question. But to find a date by serial number, there is a Parker Gun collector website that has a list of serial #'s and date of manufacture. The website is : http://www.parkerguns.org/