>>717954Yes, 3-state is high/low/high-Z, meaning sending 1, sending 0 or being disconnected from the circuit. By putting either of your input or output at a high-Z state, the other can operate without being affected by it.
If we take your image's component for example, the setup proposed with the single pin implies that the legs 3 and 5 are shorted and are connected to the "single pin". Sending "1" into either 1 or 4 relays 2 to 3 or 5 to 6 respectively. As such, 2 is your output leg and 6 is your input leg. You need to set up the signals that go into 1 and 4 so that you either get an input or an output but not both at the same time. That could be achieved by putting a NOT gate between 1 and 4, but that would mean you don't have a generalized high-Z state.
That's the basic setup that should maybe get you started. I would have gone further, but I didn't understand the requirements in your assignment exactly.