How do I know what direction the side of a part under the player's mouse is facing?

So, I have a tool that should spawn a poster on any wall the player clicks at. I got everything right but I can't seem to get the correct rotation of the poster to match up with the direction that wall is facing. How do I make that poster face whatever direction the side of any other part is facing? Not what the whole part is facing, only the specific side of it that was clicked on by the player.

Local Script:

local replicatedStorage = game:GetService("ReplicatedStorage")
local spawnPoster = replicatedStorage:WaitForChild("SpawnPoster")
local player = game:GetService("Players").LocalPlayer

player:GetMouse().Button1Down:Connect(function()
	if (player.Character:FindFirstChild(script.Parent.Name) and player.Character[script.Parent.Name]:IsA("Tool")) then
		spawnPoster:FireServer(player:GetMouse().Hit)
	end
end)

Server Script:

local replicatedStorage = game:GetService("ReplicatedStorage")
local spawnPoster = replicatedStorage.SpawnPoster
local Poster

spawnPoster.OnServerEvent:Connect(function(player, position)
	print(position)
	Poster = replicatedStorage.Poster:Clone()
	Poster.Parent = workspace.Posters
	Poster.CFrame = CFrame.new(Vector3.new(position.x, position.y, position.z), Vector3.new(math.rad(position.x), math.rad(position.y), math.rad(position.z)))
end)