Billboard GUI Issue?

camera = game.Workspace.CurrentCamera -- camera
part = -- location of the part containing the BillboardGui
game:GetService("RunService").RenderStepped:connect(function() -- refresh every 0.0167 seconds
	if (camera.CoordinateFrame.p - part.Position).magnitude < 20 then -- checks if the distance is smaller than 20 studs
		part.BillboardGui.Enabled = true -- makes it visible
	else
		part.BillboardGui.Enabled = false -- makes it invisible
	end
end)

This script will check if the camera position is in the limit of 20 studs. If you want to check the character, then just change this

camera = game.Workspace.CurrentCamera -- camera
	if (camera.CoordinateFrame.p - part.Position).magnitude < 20 then

for this

character = game.Players.LocalPlayer.Character
	if (character.Head.Position - part.Position).magnitude < 20 then

. Magnitude is very useful.