The term 'MAKE AN APPOINTMENT' can be solved by the four-letter word 'HIRE'. This term is used to describe the process of engaging someone to do a job or task. It is often used in the context of employment, where an employer hires an employee to work for them. It can also be used in other contexts, such as when a customer hires a service provider to do a job. In any case, the act of hiring someone involves making an appointment with them to discuss the job and its details.