I found this sentence in a book: "The battles of august, 1918, would have been child's play to bear." (commas)?

Yes, the commas are incorrectly used here.

It should be like this: The battles of August 1918 would have been child's play to bear.

Let's start with "the battles of August, 1918" first. There shouldn't be a comma between 'August' and '1918' because August isn't a day, it's a month. Your book says: Use a comma to separate the DAY OF THE MONTH from the YEAR, and it's correct. Once again, August isn't a day, so no need to put a comma between it and the year.

Next is "August 1918, would have been...". No comma should be put between '1918' and 'would', because "the battles of August 1918" and "would have been child's play to bear" are not separate clauses/sentences.

Example of placing a comma between clauses: Kathleen waved at her friends, tears trailing down her cheeks.

Onto your book: If any part of the date is omitted, leave out the comma. This is right. August 1918 doesn't have a particular day in it, so just omit the comma between the month and year.

I hope you understood that ^_^ It sounds confusing to me...

My heavens, I never have been flashed, but I did unintentionally flash a few folks once. I was in the hospital some time back and decided to take a stoll to the vending area. Well, I wasn't thinking about what I was wearing and, let's just say that those hospital gowns don't leave a lot to the imagination on the backside. The nurse came up from behind me and put a blanket over my shoulders . . . I was wondering why it was a little drafty back there!