What is the most appropriate word to fill in the blank: They decided to __________ a meeting to discuss the upcoming project deadline.

The most appropriate word to fill in the blank is "schedule." This choice indicates that the individuals are planning to set a date and time for the meeting, which aligns perfectly with their intention to discuss important matters regarding the project deadline. Scheduling a meeting indicates proactive behavior and readiness to address an upcoming challenge, whereas the other options imply different actions: postponing would suggest delaying a meeting that has already been set, canceling would indicate that a meeting is no longer taking place at all, and avoiding suggests evading the meeting altogether, which does not apply in this context. Thus, "schedule" fits the intended meaning best, reflecting a clear initiative to engage in discussion about the project.