If I exercise this clause on 3-29-2018 can this apply thru 9-30-2018, or only until 9-28-2018?
The FAR does not have a definition for "month". According to FAR 1.108(a), "Undefined words retain their common dictionary meaning." The WordNet Dictionary defines month as follows:
Noun 1. month - one of the twelve divisions of the calendar year; "he paid the bill last month"
Synonyms: calendar month
2. month - a time unit of 30 days; "he was given a month to pay the bill"
Meriam-Webster defines month as "a measure of time corresponding nearly to the period of the moon's revolution and amounting to approximately 4 weeks or 30 days or ¹/₁₂ of a year."
Based on these definitions, a "month" is equivalent to 30 days. Therefore, "six months", as used in FAR Clause 52.217-8 -- OPTION TO EXTEND SERVICES, would be equivalent to 180 days based on the common dictionary definition of month.