June, 1948
When was the serial? They all have serials. They were made from 1936-54 and have date code stamps on the barrel which can be looked up on the manufacture date link on the Remington Society of America.
Check date code on barrel - see related links
Production started in 1955 and continues.... The date (month/year) can be determined by the data code stamped on the barrel. A diagram of the date code location and a table explaining it can be found the the Remington Society of America's (collector site) in the manufacture date link. http://www.remingtonsociety.com
1946, it will be date code (month/year - letters) on the left side of the barrel. You can look this up under the manufactured date on the Remington Society of America site.
It's date code stamped on the barrel, see related links for information on the Remington Society of America.
The date code for a Model 336 with an F as the prefix is 1948.
March 1940
Need to check the barrel date code. Remington Society of America, Manufacture date link has all the details.
Check date code, see related links
1932, date code stamped see related links
Check date code on barrel, see related links