My script doesn't work when I touch the trigger, What's the problem?

You're changing it via StarterGui not PlayerGui, however you should consider the following:

Handle UI work on the client rather than server. Also you've got your player variable, but have not checked if it's an actual Player.

Coins.Changed:Connect(function()
    plr.PlayerGui.StatsUI.ImageLabel.CoinStat.Values.Text = Coins.Value
end)

like pwx stated in his answer, you never stated if hit.Parent actually has a player, because of that, if the hit doesn't have a player it returns nil (nothing), which can cause your script to error. also, you are meant to edit the player gui, not starter gui.

so here is a fixed version of your script:

local multi = 2

db = false

script.Parent.Touched:Connect(function(hit)
    if db then return end -- if cooldown active then the function will not do anything
    db = true
    local plr = game:GetService("Players"):GetPlayerFromCharacter(hit.Parent)
    if plr == nil then return end -- if no player from the thing that touch it then function do nothing
    local xp = game:GetService("Players").Values.XPValue
    local coins = plr:FindFirstChild("leaderstats").Coins

    coins.Value = xp.Value * multi

    coins:GetPropertyChangedSignal("Value"):Connect(function()
        plr:FindFirstChild("PlayerGui").StatsUI.ImageLabel.CoinStat.Values.Text = coins.Value -- player.playergui instead of startergui
    end)
end)