Whereupon he promised with an oath to give her whatsoever she should ask.

So he gave her his word with an oath to let her have whatever she might make request for.

οθεν μεθ' ορκου ωμολογησεν εις αυτην να δωση ο, τι αν ζητηση.

Whereupon he promised with an oath to give her whatsoever she would ask.

Whereupon he promised with an oath to give her whatever she should ask.