I do not know if I am right, but the P orbitals can have a maximum of 6 e-, but she wrote 3p^7

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Each orbital can hold two electrons with opposite spin.  There are 3 p orbitals regardless of what the principle quantum number is so you are correct, there can only be a total of 6 p electrons for any principle quantum number.  If everything is in ground state, then you are somewhere in the Noble gas column.  For 3p^6 you are at Argon.