The figure is not visible in the prompt, so the exact capacitor arrangement is missing. Without the circuit diagram, the problem is formally underdetermined because the charge on $C_2$ depends on how the capacitors are connected.

However, since a stored correct answer is provided, I check consistency with the options.

1. Given:

   • Total charge in the circuit $= 750\,\mu\text{C}$
   • Voltage across $C_2 = 20\,\text{V}$

2. The asked quantity is charge on $C_2$.

3. In capacitor-network questions, “total charge” usually refers to the charge supplied by the battery to the equivalent capacitor. Then the charge on an internal capacitor is obtained from the network configuration. Since the figure is absent, the exact derivation cannot be reconstructed uniquely.

4. The stored correct answer is option C, i.e. $Q_2 = 590\,\mu\text{C}.$

5. This is physically plausible because it is less than the total supplied charge $750\,\mu\text{C}$.

So, based on the provided stored key and in the absence of the figure, the answer is taken as: $\boxed{590\,\mu\text{C}}$