Activate Troubled Healer by sacrificing Arid Archway.
When Arid Archway dies, Toph, Hardheaded Teach triggers, returning Arid Archway from your graveyard to the battlefield tapped.
When Arid Archway enters, it triggers, returning the artifact cast in step 1 from the battlefield to your hand, as it's a land due to Toph, the First Metalbender.
Resolve the Troubled Healer ability
Repeat.
This intricate loop transforms a zero-mana artifact into an engine of endless triggers by leveraging the unique type-changing magic of Toph, the First Metalbender, which turns your nontoken artifacts into lands. When you cast that artifact, Toph, Hardheaded Teacher triggers to earthbend Arid Archway, priming it for sacrifice to Troubled Healer's prevention ability. Because Arid Archway is a land, sacrificing it triggers Toph, Hardheaded Teacher to return it to the battlefield, where its own entry trigger forces you to bounce the artifact back to your hand as a land—ready to be recast and repeat the cycle indefinitely.