It is easy to find the author - Lao Tzu. But I lost hope trying to find the context, e.g. the book of the quote's origin. Hoping Stack Exchange philosophers can provide the answer.
See e.g. Wordsworth Edition with A.Waley translation,1997, page 66.
From a different translation: Lao Tzu, Te-Tao Ching: A New Translation Based on the Recently Discovered Ma-wang-tui Texts (Robert Henricks editor, 1992, Ballantine Books):
The most difficult things in the world begin as things that are easy;
The largest things in the world arise from the minute.
天下難事必作於易，天下大事必作於細 Tianxia nanshi bi zuo yu yi Tianxia dashi bi zuo yu xi
I would translate this: difficult things in the world must be done with ease, and great things in the world must be done done with care/(pay attention to details)... In the context of ch. 63 (:when) "difficult...with care" then the derails make the difficult task easy." For example: when sages are well versed in the canons, it is easy for them to explain a difficult text to a layman.