How many 1969 formula S 383 factory 4 speed barracudas made?

There's no definitive, publicly available record of the exact number of 1969 Plymouth Barracudas built with the 383 cubic inch engine and a factory four-speed transmission. Production numbers from that era were often not kept with the level of detail we see today. Various sources offer estimates, but none are considered completely accurate. You'll likely find conflicting information depending on the source.