why doesn't my ontouch part script work in game when it works in roblox studio's solo test?

The problem is, you can't use "LocalPlayer" inside a server script. This is because what is done on a server script is done through the server, and what's done on a local script is done through the client (hence the name "local"). To fix this, don't use local player.

You need to keep everything how it is, but make it use a different way of finding the player. What you should be using to make this work is something called GetPlayerFromCharacter. There is an example located on the wiki, so I'm not really gonna explain what it does. I will fix your script in this answer, but please read over the wiki link I posted to understand what I did.

local die = script.Parent
local debounce = false

script.Parent.Touched:Connect(function(hit)
    local p = game:GetService("Players"):GetPlayerFromCharacter(hit.Parent) --using GetPlayerFromCharacter

    if p.Character:FindFirstChild("Head") and not debounce then --same as debounce == false
        debounce = true

        local b = Instance.new("Explosion")
        b.BlastPressure = 1
        b.BlastRadius = 1
        b.Position = p.Character:FindFirstChild("Head").Position
        b.Parent = workspace --I prefer using workspace rather than game.Workspace
        p.Head:Destroy() --don't use Remove(), use Destroy()

                wait(2) --add a wait so it doesn't break the script

        debounce = false
    end
end)