Aluminium can be extracted from bauxite by which of the following process?

The correct option is C

By electrolysis of its oxide.

Bauxite ore ($A{l}_2{O}_3$, impure) is first purified to form pure $A{l}_2{O}_3$. And then it goes through the Electrolysis process to give Aluminium metal at the cathode. Aluminium cannot be extracted by heating alone because aluminium is very reactive and it hangs on with oxygen and does not form aluminium metal. And aluminium is more reactive than carbon and hydrogen. So carbon and hydrogen will not be able to replace aluminium from its oxide.