There are various synonyms for the phrase "held inquiry." One commonly used term is "conducted investigation," which implies a thorough and comprehensive examination of a situation or event. Another synonym is "held hearing," indicating a formal or legal proceeding to gather information or testimony. "Carried out examination" is another option, suggesting a deliberate and methodical process to assess a given situation. "Undertook an inquiry" is another synonym, emphasizing the initial steps taken to investigate a matter. Overall, these synonyms highlight the rigorous and systematic approach required when holding an inquiry or investigation.