The electrochemical extraction of aluminum from bauxite ore involves

The industrial extraction of aluminium from bauxite involves three main stages.

1. Purification of bauxite by the Bayer process:
  a) Digestion - powdered bauxite is treated with hot concentrated caustic soda. $$Al_2O_3 + 2\,NaOH + 3\,H_2O \rightarrow 2\,Na[Al(OH)_4]$$.   This directly supports Option C because $$Al_2O_3$$ really is dissolved in hot aqueous $$NaOH$$.

  b) Precipitation - the clear sodium aluminate liquor obtained above is cooled and bubbled with $$CO_2$$.     $$2\,Na[Al(OH)_4] + CO_2 \rightarrow Al_2O_3\!\cdot\!3H_2O \downarrow + 2\,NaHCO_3$$.   This hydrated alumina is filtered, washed and ignited to get pure $$Al_2O_3$$.   Thus Option B is also correct.

2. Electrolytic reduction by the Hall-Héroult process:
  Pure $$Al_2O_3$$ has a very high melting point, so it is dissolved in molten cryolite $$Na_3AlF_6$$ (sometimes with $$CaF_2$$) to lower the melting point and increase conductivity.
  Electrolysis is carried out in a carbon-lined steel cell. Molten aluminium is deposited at the cathode, while the carbon anode is oxidised, producing $$CO_2$$:   Cathode: $$Al^{3+} + 3e^- \rightarrow Al(l)$$   Anode: $$C(s) + 2\,O^{2-} \rightarrow CO_2(g) + 4e^-$$.   Hence Option D is correct.

3. Assessment of the remaining option:
  Option A suggests directly reducing $$Al_2O_3$$ with coke above 2500 °C. Such a reaction is thermodynamically difficult because aluminium forms a highly stable oxide; coke cannot reduce it even at those temperatures. Therefore Option A is incorrect.

Therefore, the processes actually used in aluminium extraction correspond to:
Option B (neutralisation with $$CO_2$$), Option C (digestion in hot $$NaOH$$), and Option D (electrolysis of $$Al_2O_3$$ + $$Na_3AlF_6$$).

Final answer: Option B, Option C, Option D.