In order to have a good load regulations, the value of series resistance R should be such that the current through the Zener diode is much larger than the load current. For this, we select the Zener current five times the load current, i.e.,
`I_(Z)=5xx4=20mA.`
The total current through series resistance
`R=I_(Z)+I_(L)=20+4=24mA.`
The voltage drop across `R=10.0-6.0=4.0V`
Therefore, `R=(4.0V)/(24mA)=167Omega`