when you quote him the question appears instead of 32,
To do both you only need to press the smart button (lb)
to do the moves manually you have to use a combo of jump and crouch, I have no idea how to manually mantle personally
Doing things manually, is more about timing, since you can do things faster if you do them manually.
Ex. (using smart only) running towards a low wall, you reach it, you climb/mantle over it.
(manually) running towards a low wall, you jump before you reach it, and quickly vault over the top, eliminating having to climb it.
To mantle manually, I am not sure, but I would think it would be to hold down jump to initiate a climb or vault.