Final answer:
A case study is the most appropriate research method for studying a unique situation like a child growing up in a household where four languages are spoken, as it allows for an in-depth, detailed analysis of the individual case.
Step-by-step explanation:
If a researcher wanted to study a unique situation, such as a child growing up in a household in which four languages are spoken, the most appropriate research method is a case study. A case study allows for an in-depth analysis of a single event, situation, or individual, which is ideal for investigating the complex dynamics of multilingual development in a specific context. In conducting a case study, researchers might examine existing sources such as documents, archival records, engage in both direct and participant observation, and conduct interviews to gather rich, detailed information.
Other research methods like surveys, correlational studies, or cross-sectional studies may not provide the same depth of understanding because they are generally used to collect data from larger populations or to study relationships between variables, rather than exploring the intricate details of a specific case.