How do I check if a certain item is in a player's inventory?

You only spawn Cardboard because you're comparing Obj (which is a table) to a string, which will be false. On the else statement, you finally set Object to the Cardboard, so it will always spawn the cardboard. You can also use a for loop to reduce the number conditionals that you have to write.

local Spawner = Vector3.new(157.324, 0.974, 26.163)
local Clicker = script.Parent 
local ObjectSpawn = script.Parent.Parent.Spawn 
local debounce = false


Clicker.MouseClick:Connect(function(player)
	if not debounce then
		debounce = true

		local Backpack = player:FindFirstChild("Backpack")
    		if Backpack ~= nil then
        		print "Check"

			--I assume you want to spawn one random item from the player's inventory.
			local Item= {}			

local Obj = Backpack:GetChildren()
			
			for _,v in pairs(Obj) do
				print(v.Name)
				table.insert(item, v)
			end        		
			
			--If the player has the item then clone a random one to workspace.
			if #Item ~= 0 then
				local Object = game.ReplicatedStorage:FindFirstChild(Item[math.random(1,#Item)].Name)

				if Object then
					Clone = Object:Clone()
					Clone.Parent = workspace
					Clone:MoveTo(Spawner)
				end
			end
		
			script.Parent.Parent.BrickColor = BrickColor.new("Persimmon")
			wait(12)
			script.Parent.Parent.BrickColor = BrickColor.new("Shamrock")
			debounce = false

		end
	end
end)