A double displacement reaction, also known as a metathesis reaction, involves the exchange of ions between two reacting compounds to form two new compounds. Typically, this type of reaction occurs when two ionic compounds in aqueous solutions react, resulting in one product being insoluble and precipitating out.

Among the given options, let's analyze them for confirming a double displacement reaction:

1. Formation of a precipitate when two solutions are mixed: This indicates a double displacement reaction. When solutions of two soluble ionic compounds are mixed and form an insoluble precipitate, it is a classic example of a double displacement reaction.
2. Formation of a single product from two reactants: This describes a synthesis or combination reaction where multiple simple substances combine to form a single compound, not a double displacement reaction.
3. Release of hydrogen gas when metal reacts with acid: This depicts a single displacement reaction where a more reactive metal displaces hydrogen from an acid, not a double displacement reaction.
4. Colour change due to displacement of metal: This is indicative of a single displacement reaction where one element displaces another element in a compound. It's not a double displacement reaction.

The correct answer is: Formation of a precipitate when two solutions are mixed. This is because the formation of a precipitate confirms the exchange of ions characteristic of a double displacement reaction.

In summary, double displacement reactions are characterized by the exchange of ions between two compounds leading to the formation of a new product, often a precipitate. The occurrence of a precipitate is the key observation that confirms a double displacement reaction.