The value of $R_{S}$ should be such that the current through the Zener diode is much larger than the load current. This is to have good load regulation. Choose Zener current as five times the load current, i.e., $I_{z}=20 \,mA .$ The total current through $R_{S}$ is, therefore, $24\, mA$. The voltage drop across $R_{S}$ is $10.0-6.0=4.0 \,V$. This gives $R_{S}=4.0\, V /\left(24 \times 10^{-3}\right) A =167\, \Omega .$ The nearest value of carbon resistor is $150\, \Omega .$ So, a series resistor of $150 \,\Omega$ is appropriate. Note that slight variation in the value of the resistor does not matter, what is important is that the current $I_{2}$ should be sufficiently larger than $I_{L}$