Panharmonicon's ability reads: 'If an artifact or creature entering the battlefield causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.' This means any triggered ability that uses the template 'when [artifact] enters the battlefield' will trigger twice when that artifact enters under your control while you control Panharmonicon.
This works because Panharmonicon creates a replacement-like modification to the number of times a trigger is placed on the stack. Per CR 603.2, triggered abilities trigger whenever their trigger condition is met. Panharmonicon effectively doubles that trigger event for qualifying ETB triggers, placing two instances of the ability on the stack instead of one.
Note that Panharmonicon only doubles triggers from permanents you control. If an opponent controls a permanent with an ETB trigger, and an artifact enters your battlefield, Panharmonicon will not double the opponent's trigger (CR 603.2, 609.7).
Concrete example: You control Panharmonicon and cast Solemn Simulacrum (an artifact creature). Its 'when Solemn Simulacrum enters the battlefield, you may search your library for a basic land card...' ability triggers twice, so you search for and put two basic lands onto the battlefield tapped.
Both triggered abilities are independent once on the stack — they resolve separately, and each can be countered or responded to individually (CR 603.2, 116.3a).
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.