Half a year is a semester, i.e. (literally) 6 months. Since it’s often wrongly thought to derive from semi- ‘half’, there’re contradicting definitions of similar terms: Both a trimester and a (rare) quadmester are either 3 months, i.e. a fourth of a year, or a third of a year, i.e. 4 months. The definitions are mutually exclusive, that means the terms never mean the same duration in the same context. These are academic terms that usually subdivide the academic year from autumn to autumn, not the calendar year. Human pregnancies are also often divided into 3 three-month trimesters.
In economics and accounting, a quarter or quarter-year is often used, which is either defined as 3 months or as 13 weeks, i.e. 90–92 days. The possible alternative term fourth is not being used, as far as I know.
What would you call a sixth part of the calendar year, i.e. 2 collective months or about 60 days?
From other European languages, I’d assume sextal, but the OED only lists ‘base 6’ as a meaning of that word (like ‘octal’) and it’s not quartal (or tertial and quintal) in English but quarter – alas, sexter seems just wrong. Sometimes the Romance x becomes an s, and sester used to be a (Middle) English measure indeed. I could also go Greek (hexa-) instead of Latin.
I guess double-month or di-/bi-month could also work. A neologism is fine as long as it’s understandable and doesn’t raise wrong associations like a six-month span.