The choices for the 1964 Falcon are .....
..the brand new 3 speed C-4 automatic introduced for the 1964 model year
...or the older 2 speed Ford-O-Matic used from 1959 to 1964
The C-4 would have a "6" code on the warranty plate
Will have a metal tag on a servo cover bolt on the left side of the case. In the upper left corner of the tag is the letters PCV
Has a relatively square drain pan will 11 bolts
The 2 speed will have a "PBS" stamped into the right rear of the main case
Has a single piece case
The pan is oddly shaped with a hump and has 14 bolts
The above is a Ford-O-Matic two speed automatic transmission commonly used behind a six cylinder engine from 1959 to 1964.
Many of these were scrapped in later years so it is becoming a more of a rarer transmission