The Marlin model 24 pump action shotgun was produced by Marlin firearms company from 1908-1915.
No way of knowing unless you provide the model number of the Marlin rifle in question,along with the serial number.
By the serial number.
It is almost impossible to determine what a model number is based only on the serial number.
can't be answered without the serial number.
Yopu wont find a serial number anywhere, because these guns were made before the 1968 Gun Control Act which required .22 rimfire rifles to have a serial number. Prior to that many .22's didn't have serial numbers, although some makers did for their own use. Marlin only did so on lever and pump action .22's.
Your Marlin model 38 pump action 22cal rifle was made between 1920-1930.
You have a Marlin model 1896 slide action shotgun, however, it is a Blackpowder shotgun and you will need brass hulls.
That is the model number the serial number is stamped behind the hammer
http://oldguns.net/sn_php/marlinlookup.php returns 1886 as the date for this serial number.
The Marlin firearms company produced pump action shotguns from 1898(the Marlin model 1898)all the way up to 1985(The model 120 Magnum shotgun).during that time span Marlin made 17 different model pump action shotguns.
The Model 37 pump rifle made by Marlin Firearms was made from 1923 to 1931. The production records are gone, but it is known that the highest serial number on this gun was in the 12,000 area. Based on that, this gun was probably made in 1927 or 1928.