How do I make a part unanchor when an explosion touches it?

What you are looking for is the Hit event of the Explosion object. This event will fire when your specified Explosion object hits a BasePart.

Knowing this, you can Connect() a function that unanchors the touched BasePart at the occurrence of this event.

--[[
	hitPart is the part that was touched by the explosion
	distance is the distance of the part from the explosion
--]]
explosion.Hit:Connect(function(hitPart, distance)
	hitPart.Anchored = false
end)