Answer:
A : Harding was known for his terrible use of English. His writing was like dogs barking idiotically through endless nights.-----
This is used incorrectly because not only is the phrase un-quoted but Mencken wasn't recognized for bringing forth the quote.
B : Harding was known for his terrible use of English. According to H.L.Mencken, Harding's writing brought to mind, "dogs barking idiotically through endless nights."
This quote is used correctly because it not only shows where the quote came from but it also uses quotes. ("")
C : Harding was known for his terrible use of English. His writing brought to mind, "dogs barking idiotically through endless nights."
This is not a correct way to use this quote because it does not acknowledge where the quote came from.
D : Harding was known for his terrible use of English. According to H. L. Mencken, Harding’s writing brought to mind dogs barking idiotically through endless nights.
This an incorrect way to use the quote from Mencken because what he said isn't quoted.
Hope this helps!