The distance to Alpha Centauri, which is the closest star system to our solar system, is approximately 4.37 light-years. This means that light, or any other electromagnetic signal, would take about 4.37 years to travel one way between Alpha Centauri and Earth.
If we were somehow able to miraculously travel to Alpha Centauri in 6 years, it would still take a minimum of 4.37 years for a signal to reach Earth from the deployed rover, assuming the rover is capable of transmitting a signal at the speed of light. Similarly, it would take another 4.37 years for a signal from Earth to reach the rover.
In total, the round-trip communication time would be around 8.74 years. This assumes that there are no significant delays or distortions in the transmission due to interference, cosmic phenomena, or limitations in technology.
It's important to note that our current technology and understanding of physics do not allow for spacecraft to travel at speeds anywhere near the speed of light. Therefore, the scenario you describe is purely hypothetical at this point, as we do not have the capability to reach Alpha Centauri in such a short time frame.