"Does the Cisco Catalyst 2960-X Series support IPv6?"
Yes. Cisco Catalyst 2960-X Series Switches are IPv6 certified. These switches with LAN Base software support, such as Catalyst 2960-X Switch WS-C2960X-24TS-L :
IPv6 host
IPv6 management
IPv6 static routing
IPv6 MLD v1 and v2 snooping
IPv6 port-based ACLs
IPv6 router ACLs
IPv6 QoS
IPv6 First Hop Security (RA guard, source guard, and binding integrity guard).