Which electron configuration represents an
atom of magnesium in an excited state?
(1) 2–7–3 (3) 2–8–2
(2) 2–7–6 (4) 2–8–5

Atomic number of magnesium is 12. That implies that in ground state magnesium has 2 electrons in the first level, 8 electrons in the second level, and 2 electrons in the third level. That is represented by 2 8 2. That the atom is in an excited state means that one electron (at least) is a upper level than where it is in grounded state. That situation is represented by the option (1) 2 7 3, where one electron from the second level has been promoted to the third level.

Yes you are correct use the scientific method