There are several synonyms for the word "under-manned," which is used to describe a situation where there are too few personnel to carry out a task or job effectively. One common synonym is "short-staffed," which implies a shortage of employees or resources. Another alternative is "understaffed," which suggests a lack of personnel to properly manage or operate a business or organization. "Inadequately staffed" is another possible synonym, indicating a situation where the current staffing levels are insufficient to meet the needs of the job or project. Overall, these synonyms highlight the importance of having the right number of personnel to successfully complete any task or venture.