Use the Zener regulator condition

In a Zener voltage regulator, the output voltage across the load is approximately equal to the Zener breakdown voltage: $V_Z = 6\text{ V}$

Identify when Zener current is maximum

The Zener current becomes maximum when the input voltage is maximum, because then the series resistor has the largest voltage drop.

Given: $V_{in}^{\max} = 16\text{ V}$

Use the circuit relation

From the figure, the series resistor is $4\,\text{k}\Omega$ and the load current is negligible / not affecting the maximum Zener current calculation.

So the current through the resistor is $I = \frac{V_{in}-V_Z}{R}$

At maximum input voltage, $I_Z^{\max} = \frac{16-6}{4\times 10^3}$

$I_Z^{\max} = \frac{10}{4000} = 2.5\times 10^{-3}\text{ A}$

$I_Z^{\max} = 2.5\text{ mA}$

Match with options

$2.5\text{ mA}$ corresponds to Option C.

Compare with stored answer

Stored correct answer is A: 3.5 mA, but the calculation gives C: 2.5 mA.

Hence, I do not agree with the stored answer. The likely correct answer is C.