First of all, I'm no expert on IPv6.
Every Ethernet packet contains the information about its next layer in the Ethernet Type field. It tells you whether its an IPv4 packet, IPv6 packet, ARP packet or other.
IPv4 networks have IPv4 packets and IPv6 network have IPv6 packets. Of course your LAN (Etherent) can handle both IPv4 and IPv6, but usually each network has one kind of network protocol...
Routers that connect different networks can (and should) translate IPv4 packets to IPv6 packets (and their addresses).
Have you tried sending packets from your local IPv4 network (or host) to an IPv6 address?