How do you use moveto but only allow the character to move along a certain path?

Use Pathfinding,

local TheFirst = script.Parent.TheNpc.Humanoid -- Change TheNpc to your npc's name

local In = game.Workspace.FirstBrick  -- Start Point
local Out = game.Workspace.SecondBrick -- Finish Point

local Click = game.Workspace.Click -- I clickable part to make him move

local path = game:GetService("PathfindingService"):ComputeRawPathAsync(In.Position, Out.Position, 500) -- Don't ask me "Why 500?" I don't know.
local points = path:GetPointCoordinates()


Click.ClickDetector.MouseClick:connect(function()
	for _, point in pairs(points) do
		print("moving to: ", point)
		TheFirst:MoveTo(point)
		-- Don't try moving to the next point until we are close enough to the current point in the path
		repeat
			local distance = (point - TheFirst.Parent.Torso.Position).magnitude
			wait()
		until distance < 3
	end
end)

1. Change TheNpc to your npc's name
2. Make two bricks in the workspace , one called FirstBrick (Start point) and another one called SecondBrick (FinishPoint) 3)Make a brick in the workspace called Click, with a click detector inside.
3. Place the script in the workspace.

TIP: The npc will take the fastest way to the finish point.

If that doesn't work check: http://wiki.roblox.com/index.php?title=Pathfinding