A voltage regulating circuit consisting of Zener diode, having...

The maximum current through the Zener diode is determined by its maximum power dissipation: I_{Z,max} = \frac{P_\max}{V_Z} = \frac{0.4}{10} = 0.04 A.
The protective series resistance must limit the current such that the Zener operates safely. Using Ohm's law across the series resistance and Zener when the Zener carries maximum current:
$R_s = \frac{V_{in} - V_Z}{I_{Z,max}} = \frac{15 - 10}{0.04} = \frac{5}{0.04} = 125$ Ω