The electron configuration of the atom is $1s^2$ $2s^2$ $2p^4$. There are 8 electrons in total and the electron configuration corresponds to a neutral atom, so the atomic number must be 8 also. The element is oxygen and it lies in group 16 OR since the atom has 6 valence electrons, its element should be located in group 16.
There are two subshells so the period number is 2. This question is moderately difficult as the student must deduce that the number of electrons is equal to the atomic number or determine which of the orbitals are part of different shells, without the assistance of orbital labels.