What is the difference between "a half year" and "half a year"?
I think both mean 6 months.
What separates them?
I'll appreciate you very much if you explain this giving some examples.

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つねさん、そのひょうけんが同じです。

Answer

Hi, Tsune. Yes, they both mean six months. However, I rarely (if ever) hear "a half year" in American English. Also, I feel it is more proper to say "half of a year" instead of "half a year."