What is the yearly residency requirement for a green card holder?

The answer to your question is significantly more complex than calculating six months in a calendar year or six months in a year with a different starting date. It is not clear whether your question is asking about maintaining Permanent Resident status or about eligibility for petitioning for naturalization. Generally, a single absence of 180 days will create a (rebuttable) presumption that one has abandoned his/her residence in the U.S., and a single absence of a year or longer will create a legal determination of abandonment of residence in the U.S. Multiple shorter absences, even with none reaching 180 days, can create an abandonment of residence, and, making the analysis more complex, there are legal exceptions to these rules. There is no alternative to engaging an immigration attorney to learn the relevant facts specifically relating to you in order to advise about eligibilities, options and strategies.

6 months from permanent resident status. But it is not that simple, because even if you take frequent travels for 6 months, the USCIS/CBP may question validity of the status.