Which one of the following oxide dissolves in both hydrochloric acid and sodium hydroxide?

According to the question, As we know that the oxides of metal is basic in nature whereas the oxides of non-metal are acidic in nature.

Aluminium oxide is amphoteric oxide. Which works as weak acid and weak base. So it is soluble in both HCl and NaOH and forms salt. 

Whereas other options given in question are strong basic (metal oxide) in nature, so they react only with acid (HCl).