If you're asking whether a given NIC on a given OS can have both an IPv4 and IPv6 address at the same time, yes. This is more ""coexisting"" than ""using simultaneously"". Think of them as parallel network stacks -- network traffic will use one or the other but not both. If you're asking whether a given application can access a network resource with both at the same time, kinda-sorta-maybe-ish. There are methods to allow interoperability and communication between the two, but they are 2 completely separate protocols.
This great article ""Interoperability between IPv6 and IPv4"" covers it pretty well."