Can IPv6-only hosts ping IPv4-only hosts and vice versa ? How ?

For IPV4  and IPV6 coexistence

we use one of tree methods : Dual IPv4/IPv6 stacks, Tunneling, NAT Protocol Translator.

and when hosts must run one of the two protocols IPv6 or IPv4 we use NAT protocol Translator, so as Asim said its NAT-PT.

Yes, the mechanism is know as NAT-PT (Network Address Translation - Protocol Translation)

I am sharing this case study to clear your concept and helps you implement your network issue ...

https://www.ietf.org/proceedings/42/I-D/draft-ietf-ngtrans-natpt-02.txt