I have seen all the chemical formulas for the reaction between sodium hydroxide, water, and aluminium. I understand that the hydrogen gas comes from the aluminum reacting with the water and the sodium hydroxide just breaks down the aluminum oxide. But why does sodium hydroxide break it down? Also since aluminum oxide is amphoteric can you do this reaction with a strong acid instead of a strong base?
If you use a "strong acid" to break down the passive oxide you need to be careful which acid you choose. Sulfuric or nitric acid is oxidizing and thus could maintain the oxide. Hydrochloric acid would be best, among common mineral acids, for actually getting to the metal while being relatively easy to handle.
C2H6O2 is a chemical formula.
HOCH2-CH2OH is a chemical formula.
CH4 + 2O2 → CO2 + 2H2O is a chemical equation. You should learn the difference.
Reaction products are usually lower in Free Energy than the reactants. If it's helpful, then the answer to your question of why does NaOH react with Al2O3 is: because the products are lower in free energy than the reactants. In my more experienced view, this is a circular answer: of course the products have more negative delta G, but that doesn't answer "why?". Science is much better answering "how?" than "why?". But at your level of understanding, you should be aware that speaking about the oxide coating on aluminum and its reactions with acids and bases is (arguably) categorically different than speaking about Al° and its reactions. You've asked about the oxide. Al+3 exists in aqueous solution as [Al+3].6H2O with its counter ion (in HCl(aq) is would be the Cl- anion) and as [Al(OH)4]- with the counter ion (in your case it would be Na+ ). BOTH of these are stable, one in acid, one in base (it's obvious which is which, right?). So, the question is: is the dissolution of Al2O3 spontaneous in acid (in base)? The answer is:"in sufficiently low (sufficiently high) pH it is." Strong base attacks skin, so does strong acid. The reactions are different, they are NOT opposites. I don't see anything unusual in the fact that a material reacts with strong acids and strong bases. My guess is that one reason you might see a dichotomy between acids and bases is because in water solutions you don't generally have both simultaneously. (at least, since the equilibrium constant of water is 1E-14, in most solutions of chemical interest (contrasted with biologically interesting situations), either acid or base is present in overwhelming concentrations...). While dealing with Bronsted acid/bases, it's sometimes convenient to consider acids as opposites to bases, that approach has limits beyond which other definitions of acidity or basicity are more useful. HTH