Answer
$\dfrac{1}{2}$
Work Step by Step
We know that the energy stored in a capacitor is given by
$$U_C=\frac{1}{2}C(\Delta V_C)^2$$
And we are given that $C_2=\frac{1}{2}C_1$, and that $(\Delta V_{C})_2=2(\Delta V_{C})_2$.
Thus,
$$\dfrac{U_{C1}}{U_{C_2}}=\dfrac{\frac{1}{2}C_1(\Delta V_C)_1^2}{\frac{1}{2}C_2(\Delta V_C)_2^2}$$
Plug the known;
$$\dfrac{U_{C1}}{U_{C_2}}=\dfrac{ C_1(\Delta V_C)_1^2}{ (\frac{1}{2}C_1) [ 2(\Delta V_C)_1]^2}$$
$$\dfrac{U_{C1}}{U_{C_2}}=\color{red}{\bf \dfrac{1}{2}}$$
