Step 1: Recall the definition of an amphoteric oxide.
An amphoteric oxide is unusual because it can behave as a base with an acid and as an acid with a base, giving salt and water either way.
Step 2: Test aluminium oxide both ways.
\[ Al_2O_3 + 6HCl \to 2AlCl_3 + 3H_2O \] \[ Al_2O_3 + 2NaOH \to 2NaAlO_2 + H_2O \] Since it reacts with both an acid and a base to give salt and water, $Al_2O_3$ qualifies as amphoteric.
Step 3: Test zinc oxide both ways.
\[ ZnO + 2HCl \to ZnCl_2 + H_2O \] \[ ZnO + 2NaOH \to Na_2ZnO_2 + H_2O \] $ZnO$ passes the same dual test, so it is amphoteric too. Copper oxide and $SiO$ do not show this two-way behaviour, so options involving them are ruled out.
Step 4: Conclude.
The amphoteric oxides among the choices are $Al_2O_3$ and $ZnO$. \[ \boxed{Al_2O_3\ \text{and}\ ZnO} \]