Step 1: The year 1984 is a leap year, as it is divisible by 4.
Step 2: A leap year has 366 days, which means the days of the week shift by 2 days from one year to the next.
Step 3: By constructing the calendar for 1984 or using the odd-days method, it can be determined that 4 months in the year 1984 started on a Sunday.
Step 4: Hence, the correct answer is 4 months.