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The 2,8,8,18 is how many elements are in each row of the Periodic Table. Each S orbital can hold 2, P orbitals can hold 3 6 (2 each in 3 total), D orbitals can hold 10 (2 each in 5 total), and F orbitals can hold 14 (2 each in 7 total).

The first shell is just 1S, which can hold 2.

The second shell is 2S, 2P which can hold 8 total (2+6)

The third shell is 3S, 3P, 3D which can hold 18 total (2+6+10)

The fourth shell is 4S, 4P, 4D, 4F which can hold 32 total (2+6+10+14)

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