1. Use the concept of displacement current inside a charging capacitor

For a charging parallel plate capacitor, the displacement current through the entire plate area equals the conduction current in the circuit:

$I_d = I = 6\text{ A}$

2. Relate displacement current through a smaller internal area

The electric field between the plates is uniform, so the displacement current density is uniform. Hence, through a smaller area $A_0$ parallel to the plates,

$I_{d0} = I_d\left(\frac{A_0}{A}\right)$

Given:

$A = 16\text{ cm}^2, \qquad A_0 = 3.2\text{ cm}^2$

So,

$\frac{A_0}{A} = \frac{3.2}{16} = 0.2$

Therefore,

$I_{d0} = 6 \times 0.2 = 1.2\text{ A}$

3. Convert to mA

$1.2\text{ A} = 1200\text{ mA}$

Final Answer

$\boxed{1200}$