Answer:
Nam said to me that he would join the army the following month.
Step-by-step explanation:
Required
Complete the gap
"The following month" means the event is yet to happen.
To complete the gap, we make use of a verb that illustrates an event that is yet to happen.
To do this, we have:
will join
would join
.....as possible options.
However, the verb after immediate the subject (i.e. said) is in the past.
Hence, the correct option to complete the blank is "would join"