six months or in June 去以六月息者也。

Hello it's Zhuangzi Enjoyment in Untroubled Ease, first chapter.

My question:
Does he rest for six months or in June. Is Chinese the same in both cases? Does 者 mean he who goes for rest for six months?
In Chinese, although both a phrase like "six months" and the word "June" contain the characters 六 and 月, there will often be a measure word if we are talking about a specific quantity of months (i.e. in the "six months" case), the same way there will be a measure word for something like "six cats" ("六只猫") or "six books" ("六本书").

Thus, it should be generally possible to distinguish between "June" ("六月") and "six months" ("六个月"). (月 uses the word 个.) However, in this case, given the 去以, "six months" reads better ("the past six months" instead of "the past June"), at least to me as someone who does not know the context.

So I can only give you the "general" case of whether one can distinguish between what is essentially "the Xth month" and "X months" in Chinese (i.e. yes). vermillon's answer resolves the question of why I'd still presume "six months" here -- it's simply a classical Chinese thing I wasn't aware of (and it does read better).

Your assessment of 者 (as something to the effect of "he who") appears to be correct. As seen in these dictionary examples (note: the dictionary definitions itself are sometimes very unhelpful or downright probably wrong, but the examples should be fine), 者 can be appended to some sort of descriptor (whether one that takes the purpose of an adjective or a verb) to mean "the individual(s) who" or the such. For instance, 受害者 means "the individual(s) who were harmed", and 第三者 is "[those of a] third party", and the webpage gives the example "他猛击进攻者。"

I am not sure about the exact translation given the 也 which I'm having difficulty accounting for, but things otherwise sound fine.