The Pauli Exclusion principle states
in an atom or molecule, no two electrons can have the same four electronic quantum numbers. As an orbital can contain a maximum of only two electrons, the two electrons must have opposing spins.
So how can some electron shells have up to 6 electrons or more? Take the electron configuration of Magnesium. The 2p shell holds 6 electrons. How is this possible? Can you have multiple orbitals in a single electron shell?
Best Answer
A "shell" is the term for all states with the same principal quantum number $n$, but in each shell there are also possible different values for the angular momentum quantum number $0\leq \ell \leq n$, the magnetic quantum number $-\ell \leq m_\ell \leq \ell$ and the spin quantum number $m_s\in\{-1/2,1/2\}$.
So for $n>1$, 6 electrons in a shell do not violate the Pauli exclusion principle.