No assumptions involved.
The difference in the energies can only be explained by having the two outermost electrons in a different shell than the four previous ones. Thus, the outermost shell must have exactly two.
For there to be any electrons in a shell, all previous shells must be full.
The first valence shell can two electrons. For there to be electrons in any other shell, it must have these two in the first shell.
The second shell can have up to eight electrons. For the third shell to have any, these eight must be present.
Therefore, in order to have two on the outermost shell, and greater than six total, you must have at least 12: 2 in the first shell, 8 in the second shell, and 2 in the third.
You can have more than 12, by filling up the outermost shell and adding two electrons to the next shell.