How to choose correct resistor with proper wattage and ohms for 6 leds connected in a serial circuit?
Your calculations are correct. I would give the resistor somewhat headroom, power-wise: if the LEDs' voltage is a bit less than 3.2 V, like 3.1 V (the voltage can vary by much more than that!) the current will rise to 22.5 mA, and the voltage drop across the resistor to 5.4 V. Then the power will be 120 mW, so the 100 mW won't do. Overmore, 1/4 W is a more standard value, and probably cheaper.  

So go for a 240 &Omega;/0.25 W resistor.