Jun 19, 2019 / Manual for Briggs 500E series 140cc engine. #3. The new briggs push mower engines have the model number stamped into the side of the block and then appear to be painted over. Seems it is on the same side as the carb.
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The ASECC link that Skyler gave you in you last post should get you to their serials list. You are correct about interpretaion of the serial numbers--1 indicates the first unit built and the sequence follows to the end of the series. Your 149 serial on the 6H-S indicates one of the earliest of that model.
Make sure your engine is turned "OFF" and has cooled sufficiently to allow handling. Locate the engraved serial number on the side of the crank case. See below. The Date of Manufacture (DOM) indicator may be found within the engine's serial number. Locate the first four digits (all numbers) of the serial number.