有些时候比较很难区别开呢？譬如

youmake no apologies forwhat you have done.【forwhat you have done】是状语吗？

His mother offered her apologies to the Jones family【to the Jones family】是状语还是定语呢？

假如遇见类视状况，应该怎么样迅速判断呢？

《牛津》对名词apology对解释如下：

[countable,uncountable]apology ：a word or statement saying sorry for something that has been done wrong or that causes a problem

可以看出，to和for是和apology搭配的介词。也就是说to和for介词短语都是修饰apology的。

网友的二个句子中的介词短语都是定语，不是状语。