the letters' preferences are as follows:
A 642531
B 531642
C 246135
D 135246

the numbers' preferences are like so:
1 ABCD
2 ABDC
3 ACDB
4 DCBA
5 DBAC
6 DBCA

running it forwards we get:

A6 B5 C2 D1

running it backwards we get:

1ABCD
2AC
3CD.
4D.
5B
6A

which is the same thing. it's more interesting to do by hand iteratively than to see the results...