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http://imgur.com/zU72JNi
You'd like to know why I marked the two cells on the left as red? Because one of the hints is that the inner sections only contain 7 each, and I already have 6. I can only take neither or both of them to keep the column odd, and taking both puts too many cells in the section.
Thus, both of the cells on the left are empty. And since we know there's exactly one left in the circled green stuff, the very bottom cell below it must also be empty to keep the column odd.
From there, the rightmost column stays open until the end of the puzzle. Solving the entire left half leaves you with 4 remaining and only 4 places to put them.
It was only 6 hexes left - two of the ones you marked in red that are below each other and the outermost right column, except for the top one.
Anyway, thank you!