The title of this question is often mistranslated by students into the equation 8 + q = d. My question is how can I explain in *grammatical* terms where the error in reasoning has occurred? 

Students are taught early on to translate the phrase "8 more than a number" as 8 + n. What is the grammatical difference between the original sentence and that phrase which causes the mistranslation? 

Could it be the presence of the word "quarters" between "more" and "than" and if so, what would be the grammatical function of these words in the original sentence, "He has 8 more quarters than [he has] dimes," as compared to the phrase "8 more than a number"? 

Just to be perfectly clear: the topic of this question is an extremely common error in the **usage** of English to express daily counting and word problems; in particular, its mistranslation into symbols and the strictly *grammatical* reasons why this occurs.