You can create a repeatable loop: have Archaeomancer enter the battlefield to return Displace from your graveyard to your hand, cast Displace exiling Archaeomancer and Peregrine Drake, and when they return Peregrine Drake untaps lands and Archaeomancer’s ETB returns Displace again — allowing you to cast Displace repeatedly using the lands untapped by Drake. The re-entries are handled as new objects, and Drake’s triggered ability still untaps lands even though the creature is entering, so you can use those lands to pay for the next Displace. See , , , and Ruling [2022-12-08].
Step 1
Put Archaeomancer onto the battlefield (for example, cast it); when it enters the battlefield its triggered ability goes on the stack to return a target instant or sorcery from your graveyard to your hand, such as Displace .
Step 2
When Archaeomancer’s triggered ability resolves, return Displace from your graveyard to your hand (assuming it’s still a legal target).
Step 3
Cast Displace (paying its mana cost) and choose up to two target creatures you control: choose Archaeomancer and Peregrine Drake.
Step 4
When Displace resolves, it exiles those chosen creatures, then returns them to the battlefield under their owners’ control; each returning creature is a new object with no connection to the old one and Ruling [2016-07-13].
Step 5
When Peregrine Drake re-enters, its triggered ability goes on the stack and, when that trigger resolves, you untap up to five lands (you choose which lands to untap as the trigger resolves) — those lands need not be lands you controlled before the trigger resolved per Ruling [2022-12-08].
Step 6
When Archaeomancer re-enters, its ETB trigger goes on the stack; when that trigger resolves it can return Displace from your graveyard to your hand (assuming Displace is in your graveyard) so you can cast Displace again and Ruling [2018-12-07].
Step 7
Use the mana from the lands untapped by Drake to pay Displace’s cost and cast Displace again, repeating the sequence as long as you can pay its cost each time.
Resolution
If you start by putting Archaeomancer onto the battlefield so its ETB returns Displace from your graveyard to your hand, then cast Displace targeting Archaeomancer and Peregrine Drake, Displace will exile and then return those two creatures. Each that returns is a new object and will cause its ETB to trigger; Peregrine Drake’s ETB can untap up to five lands (you choose which as that trigger resolves) and Archaeomancer’s ETB can return Displace from your graveyard to your hand again. That permits repeating the sequence (casting Displace each time) using the lands untapped by Drake to pay Displace’s cost. Relevant rules: , , , and Ruling [2016-07-13], Ruling [2018-12-07], Ruling [2022-12-08].
