Cat6 network cable is shielded but the terminals are pure plastic. Where does the ground wire go?

Answer 1

Proper shielded RJ45 plugs have a metal shield around the actual plug. That provides the grounding for the shielded cable to the metal case of the device it plugs into.
Without the proper shielded plug, your cable is "not shielded" any longer, it is just a simple Cat6 cable at that point.

Answer 2

into the earth and soil