Distinguished Conjurer does not have summoning sickness.
({4} magic symbol) ({W} magic symbol) available.
Steps
Activate Distinguised Conjurer by paying ({4} magic symbol) ({W} magic symbol) and tapping it, blinking Ratchet, causing it to enter the battlefield as Ratchet, Field Medic.
When Ratchet, Field Medic enters the battlefield, Preston and Distinguished Conjurer trigger.
Resolve the Preston trigger, creating a token copy of Ratchet, Field Medic that is a 0/1 Illusion.
Put the nontoken Ratchet into your graveyard due to the legend rule.
Choose not to return Ratchet to the command zone from your graveyard.
When the Ratchet, Field Medic token enters the battlefield, Distinguished Conjurer triggers, causing you to gain 1 life.
The Ratchet, Field Medic token triggers, causing you to convert it into Ratchet, Rescue Racer, and return Ratchet from your graveyard to the battlefield.
When Ratchet, Field Medic enters the battlefield, Preston and Distinguished Conjurer trigger.
Resolve the Preston trigger, creating a token copy of Ratchet, Field Medic that is a 0/1 Illusion.
Put the nontoken Ratchet into your graveyard due to the legend rule.
Choose not to return Ratchet to the command zone from your graveyard.
The Ratchet, Rescue Racer token triggers, as well as Distinguished Conjurer.
Resolve the Ratchet, Rescue Racer trigger, causing you to convert it into Ratchet, Field Medic.
Put one of the Ratchet, Field Medic tokens into your graveyard due to the legend rule.
Resolve the Distinguished Conjurer trigger, causing you to gain 1 life.