How do you hyphenate the word 'branches'? I'm intrigued between
It is only eight letters long, and is the produced plural of a word that is only six letters long, monosyllabic and from a single root, without suffix or prefix or compound parts.
As such, I'd move the entire word onto the next line, even when space was limited.
I note that Merriam Webster and Oxford Dictionaries, two dictionaries that contain hyphenation advice, both suggest that branch has no hyphenation opportunities. Branches of course only adds the -es of the plural, and one would never hyphenate at that point if at all avoidable.
If space was extremely limited, then such an unusual typographic situation would make this a matter of graphic design rather than normal typography, so the exact opposite would apply; I'd hyphenate it whichever way worked best visually with the rest of the graphic design. (In theory anyway, I'm not very skilled in such matters).
If I had a gun to my head and had to hyphenate the word as best I could, I'd probably do so as bran·ches to match the syllables and to avoid breaking on the -es, but I wouldn't be happy with it.