Step 1: Understand the rules for electron configurations, including the maximum number of electrons allowed in each subshell: s can hold 2, p can hold 6, d can hold 10, and f can hold 14 electrons.
Step 2: Examine each given electron configuration and verify that the number of electrons in each subshell does not exceed its maximum capacity.
Step 3: For the configuration 1s^2 2s^2 2p^6 3s^2 3p^6 3d^12, note that the 3d subshell is shown with 12 electrons, which exceeds the maximum allowed 10 electrons for a d subshell.
Step 4: Confirm that all other configurations respect the maximum electron limits per subshell and follow the Aufbau principle (filling order) and Pauli exclusion principle.
Step 5: Conclude that the configuration with 3d^12 is not possible because it violates the maximum electron capacity rule for the d subshell.