how do I make a part (for example a coin) move left and right ?

What I would do is use TweenService. It is very smooth and neat.

I would also recommend editing the CFrame of the part instead of the position, so you do not run into collision problems, as CFrame ignores collision.

Here is an example of how you can use it.

local TweenService = game:GetService("TweenService")

local partToMove = script.Parent
local originalCFrame = partToMove.CFrame

local tweenInfo = TweenInfo.new(
    2, -- Time it takes to go from position to another
    Enum.EasingStyle.Linear, -- EasingStyle
    Enum.EasingDirection.Out, -- EasingDirection
    -1, -- RepeatCount (when less than zero the tween will loop indefinitely)
    true, -- Reverses (tween will reverse once reaching it's goal)
    0 -- DelayTime
) 

local goal = {
    CFrame = originalCFrame * CFrame.new(3, 0, 0) -- move by 3 studs to right -- mistake was here
}

local tween = TweenService:Create(partToMove, tweenInfo, goal)
tween:Play()

That should do it, hope I helped.

If you have further questions please let me know!