Answer:
1. 2HgO -> 2Hg + O2 is a decomposition reaction as the reactant is being split up into its constituent elements.
2. Fe2O3 + 3H2 -> 2Fe + 3H2O is a single displacement reaction as only one element is displaced which is the oxygen in the Iron Oxide.
3. 2AsCl3 + 3H2S -> As2S3 + 6HCl is a double displacement reaction, as two different elements have been displaced and reacted with another group, the Chlorine and the Sulphur.
4. 2Cu + O2 -> 2CuO is a synthesis reaction as there is one product synthesised from two reactants.
Hope this helps!