The correct answer is $\boxed{\text{D}}$.
The energy used by the battery is given by the equation $E = QV$, where $Q$ is the charge and $V$ is the potential difference. In this case, $Q = 6.28 \times 10^{18}$ electrons and $V = 20$ V, so the energy used is $E = 6.28 \times 10^{18} \times 20 = 12.56 \times 10^{19}$ J. This is equivalent to 12.56 kilojoules, or 12.56 thousand joules.
Option A is incorrect because it is too small. The energy used by the battery is proportional to the charge, and the charge in this case is $6.28 \times 10^{18}$ electrons, which is much larger than the charge in option A.
Option B is incorrect because it is too small. The energy used by the battery is proportional to the potential difference, and the potential difference in this case is 20 V, which is much larger than the potential difference in option B.
Option C is incorrect because it is too small. The energy used by the battery is proportional to the product of the charge and the potential difference, and the product of the charge and the potential difference in this case is $6.28 \times 10^{18} \times 20 = 12.56 \times 10^{19}$ J, which is much larger than the energy used in option C.