Traveling at 0.6c results in significant time dilation, where the traveler experiences time slower than observers on Earth. For a journey to a galaxy 10 light years away, the spaceship would take approximately 16.66 Earth years to arrive, while the traveler would perceive it as about 13.33 years due to time dilation. Observers on Earth would receive confirmation of the spaceship's arrival 10 years after it departed, plus the time for the signal to return, totaling around 26.66 years. Each observer perceives the other's time as slowed, but both experience their own time normally. Understanding the nuances of time dilation requires careful consideration of each observer's frame of reference.