In the Earth-2 where he encounters several doppelgangers of the people he knows.
Throughout the events of the episode, Oliver is on a mission on behalf of the Monitor to find Dwarf Star particles. But Oliver gets sucked in by seeing people like his mother Moira (Susanna Thompson) and Tommy (Colin Donnell) alive. The Monitor makes it clear that Oliver can't allow himself to get involved with the lives of the people on Earth-2. By doing so, he risks the Anti-Monitor coming for that Earth. Oliver, however, tries to have the cake and eat it too by helping Laurel Lance (Katie Cassidy) stop Earth-2's version of the Undertaking from the first season. From discovering that Tommy is the Dark Archer of Earth-2, Oliver makes it his mission to save the doppelganger of his best friend.
As Oliver got anti-matter completely destroys Earth-2, Oliver jumps back to Earth-1 with Diggle and Laurel. While Oliver never intended to get on the Anti-Monitor's radar, his actions caused Earth-2 to be destroyed.
With the Anti-Monitor fully active in taking one Earth after another, Earth-2 was always in danger no matter what. But had Oliver listened to the Monitor's warning and returned straightaway with the dwarf star particles, it could have allowed Earth-2 to live for a bit longer. It remains unknown if it was Oliver going for the Dwarf Star particles or his involvement with the events of Earth-2 that triggered the Anti-Monitor. It could have been as simple as Oliver being on Earth-2 that eventually led to the Anti-Monitor in destroying that world, hoping the Green Arrow would die with it.
But in one way or another, Oliver's choices on Earth-2 caused that world to die earlier than maybe they were supposed to. Following the premiere, Oliver has yet to travel to any other Earth in the Multiverse. Given how Earth-2 got destroyed, it is probably for the better that Oliver stays put for now. With only a couple of episodes left before the Crisis crossover, the clock is dangerously ticking. Currently, Oliver is collecting more information on the Monitor as the Crisis approaches. The latest episode "Leap of Faith" ended with Team Arrow witnessing the arrival of Mia (Katherine McNamara), Conner (Joseph David-Jones) and William (Ben Lewis) as they were transported from 2040 to 2019.