(Purpose of the series resistor is usually to drop the surplus voltage... you don't have enough in anyway
. )Or it's marginal.))
The purpose of the resistor is to limit the current since the LED turns into a short when its forward voltage is applied. This works because the resistor drops the surplus voltage of the series circuit (LED in series with Resistor).
Vresistor = Supply - Vforward = 9V - 6V = 3V
Resistor = Vresistor / Iforward = 3V / 20mA = 150ohm
Datasheet says you can run the LED to max continous current of 25mA.