High voltage!!!

The key with series capacitors is that if they are both uncharged at the beginning, the two capacitors will have the same charge at any given time. Recall the basic capacitor equation:

$Q = CV$

Therefore, for these series capacitors:

$C_1 V_1 = C_2 V_2$

What happens if we apply maximum voltage to $C_1$ (Assume $C_1 = 1 \mu F$ and $C_2 = 2 \mu F$ ).

$(1 \mu F)(6 kV) = (2 \mu F)(3 kV)$

Here we have a total series voltage of $9 kV$ , and neither capacitor is overloaded. What about the case where max voltage is applied to $C_2$ ?

$(2 \mu F)(4 kV) = (1 \mu F)(8 kV)$

Here, $C_1$ is overloaded, so this is not a viable scenario. The answer is therefore $9 kV$