How to teleport a player in a direction relative to their rotation and position?

A CFrame contains its objects axis shown here.

As these reflect the direction relation to the object we can use these to add onto the current position giving the new position with the given number of studs away.

Example:-

local function teleport(playerChar, direction, amount)
	local charCFrame = playerChar.PrimaryPart.CFrame	

	-- get the vector we want to change
	local dirctionVector
	if direction == 'left' then
		dirctionVector = -charCFrame.rightVector
	elseif direction == 'right' then
		dirctionVector = charCFrame.rightVector
	elseif direction == 'foward' then
		dirctionVector = charCFrame.lookVector
	elseif direction == 'backward' then
		dirctionVector = -charCFrame.lookVector
	elseif direction == 'up' then
		dirctionVector = charCFrame.upVector
	elseif direction == 'down' then
		dirctionVector = -charCFrame.upVector
	else
		return
	end	
	
	--  multiply the direction with the given amount to get the offset amount to add tho the CFrame
	playerChar.PrimaryPart.CFrame = playerChar.PrimaryPart.CFrame + (dirctionVector * amount)

-- test
wait(5)
teleport(game.Players.Player1.Character, 'left', 20)
end

I hope this helps, please comment if you do not understand how this code works.