WHERE IS THE SERIAL NUMBER ON BG412F - 2000 BMW 3 Series

It should have the MFG. date stamped into the I.D. plate along with the serial number . If not the serial number should have the number 17 in sequence in the serial number either at the beginning or the end.

Your Ford dealer should be able to help you.

contact the manufacturer on line and quote the machine serial number and ask for an engine serial number that engine.

This is way out of my league, but here is some info that might help.
Before 1954 there was no uniform VIN number used in the USA.
In the years leading up to 1931 Chrysler Corp and a few other car companies used a FEDCO plate on the dash or firewall for the serial number ID of the car. The car was registered by this number by some states, and some used the engine number. Starting in 1931 the serial number was changed and moved to the door post. So a 1930 car should not have a plate on the door post.
The engine number was always stamped on the block. Also keep in mind 1931 Chrysler products were carried over into the 1932 model year, including Desoto.
The serial number depended on the make and model unlike cars of today. A series 31 model started with a number 6 or 8, while a series 32 model started with letters like SA or CFS, a series K started with the letter K, and so on. Actual serial numbers were seven digits.
On most models the serial number is also stamped on the frame near the front spring support.
You can do an internet search for DeSoto FEDCO numbers and serial numbers to get a general idea of how the serial numbers were arranged. You can also contact Chrysler Historical Society to see if they have the build card for your car. The build card would have both the original engine number and serial number. There are other resources including the Antique Auto Club of America.

The radio SERIAL NUMBER is required for a code
Sometimes pressing buttons 6 & 1 together or 6 & 2 will display your Serial Number Otherwise remove the radio from the dashboard and post the SERIAL NUMBER found on a label on the casing
It usually begins with M++++++ or V++++++ ------------------------------------------------------------------------------------------------------

The password/code can only be retrieved from service center or from the dealer of the unit. Because at the back of the unit there is a serial number mentioned and the password/code only can be retrieved from the serial number. Each and every device/unit has its own serial number so one serial number code/password will not work with other serial number code password. The service center or the dealer has the list of code for the serial number so as soon as you provide the serial number he will get the password/code
Retrieved for you through the list.
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The password/code can only be retrieved from service center or from the dealer of the unit. Because at the back of the unit there is a serial number mentioned and the password/code only can be retrieved from the serial number. Each and every device/unit has its own serial number so one serial number code/password will not work with other serial number code password. The service center or the dealer has the list of code for the serial number so as soon as you provide the serial number he will get the password/code
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go to dealer supply proper docs should be free

Make sure the numbers match. The serial number is etched into the housing of the radio-starts with S/N ###etc. If you are unsure, write down the complete S/N off the radio housing and call a dealer-they will not charge to look up a radio code-it only takes a minute. If they give you a different number, then your head unit has been replaced at some point and your current card is no good. If they give you the same number, then try one more time and press seek when done. If it still does not accept it, then there may be an internal radio problem.

sometimes the previous owner might wrote it down on the owners manual but if not then you need to pull the radio out and get the serial number and call the dealer they will give you a code