How do I fill in this reaction between copper II bromide and aluminum chloride?

First, the chemical formula for the given compounds are the following:

copper (II) bromide - `CuBr_2`

aluminum chloride - `AlCl_3` 

From the solubility rules (see reference), bromides are generally soluble with a few exceptions. Bromides of copper aren't part of the exception list and copper (II) bromide is hence soluble and will be in aqueous state when added to water.

In the same manner, chlorides are generally soluble with few exceptions and chlorides of aluminum aren't part of the exception. Aluminum chloride is also soluble and will be in the aqueous state. 

Hence, all species will be in their ionic forms. Therefore, there is no reaction. 

However, if we complete the chemical equation thinking of it as a double replacement reaction, we get the following:

`CuBr_2(aq) + AlCl_3(aq) -> CuCl_2(aq) + AlBr_3(aq)` .

Note that all of the chemical species are in aqueous form. Therefore, the chemical species that are actually in solution are solvated ions - Cu2+, Br-, Al3+, and Cl-.