How do I activate a multiplier when a certain item is bought?

Inside the button, add this script. Server Script

players = game:GetService("Players") -- Gets the service called Players which is where the player is stored
script.Parent.Touched:Connect(function(hit) -- This function will fire when something has touched the button.
if hit:FindFirstChild("Humanoid") then -- Checks that what's touching it is a player
local plr = players:GetPlayerFromCharacter(hit.Parent) -- This will make the player service find the player based on the Name of the character that is touching the part
plr.Multiplier.Value = plr.Multiplier.Value + plr..Multiplier.Value -- Changes the multiplier by 1 so we can double the amount of money the player gets.
script.Parent:Destroy() -- Destroys the button so the player cant buy it again.

Next, you want to make a script to give the player leaderstats if you haven't done so already. In ServerScriptService, Make a Server Script and add a RemoteEvent inside of ServerScriptService.

game.Players.PlayerAdded:Connect(function(plr) -- Fires when a player is added to the game.
local Leaderstats = Instance.new("Folder") -- Creates a folder 
Leaderstats.Name = Leaderstats -- Changes the name of the folder to Leaderstats the name of the folder has to be Leaderstats.
leaderstats.Parent = plr -- Puts Leaderstats inside the player.
local money = Instance.new("NumberValue") -- From here down, it does the same thing, except creates number values which can be stored inside of leaderstats to represent cash and other things.
Money.Name = money
Money.Parent = Leaderstats
Money.Value = 0
local Multiplier = Instance.new("NumberValue")
Multiplier.Name = Multiplier
Multiplier.Parent = plr
Multiplier.Value = 1

After you have done this, you want to make a local script and put it in starterGui.

while wait(5) do -- fires every 5 seconds
game:GetService("ServerScriptService").RemoteEvent:FireServer() -- fires a RemoteEvent for the server.
end

after you have done this, you want to add another Server Script into ServerScriptService

script.Parent.RemoteEvent.OnServerEvent:Connect(function(plr) -- Fires when the RemoteEvent is fired.
plr:WaitForChild("Leaderstats").Money.Value = plr:WaitForChild("Leaderstats").Money.Value + 5 * plr.Multiplier -- Changes the money by 5 * the multiplier.