Marlin used many different formats over the years for making serial numbers.
You use the first 2 numbers of your 444 serial number matched to a year on that PDF file to find what year it was produced. For an example: my 444 starts with 01 so my 444 is a year 1999.
It will be easier to find the year 1999 on the PDF then see there is an 01 in the column to the left. That 01 is the first 2 characters/numbers of my serial number.
It is possible you could have a 444 with a serial number that starts with one or two letters as the first 444 was made in the 60's. I forget the exact year. A 1966 marlin would have a serial number that started with AB. I hope you find this primer helpful.