The correct option is D 150 Ω
The value of RS should be such that the current through the Zener diode is much larger than the load current.
This is to have good load regulation.
We choose Zener current as five (let) times the load current, i.e., IZ=20 mA.
The total current through RS is, therefore, 24 mA.
The voltage drop across RS is 10.0–6.0=4.0 V.
This gives,
RS=4.024×10−3=167 Ω.
The nearest value of carbon resistor is 150 Ω.
So, a series resistor of 150 Ω is appropriate.
Note : Slight variation in the value of the resistor does not matter, what is important is that the current IZ should be sufficiently larger than IL.
Hence, option (D) is the correct answer.