In the following sentence:
오늘은 날씨가 너무 더워서 밖에를 못 나가겠어요.
According to my dictionary, it seems to mean the location to which the verb does an action. But then what it the difference from just using 에? I don’t understand why the sentence above uses 를 with the verb 나가다, which seems strange.
It should look strange if you're studying Korean by the book. The correct representation of the above sentence should be "오늘은 날씨가 너무 더워서 밖을 못 나가겠어요" or "오늘은 날씨가 너무 더워서 밖에 못나가겠어요".
However, sometimes people use the term "밖에" in the place of "밖". I believe that it's because people use "밖" with "-에" so often that it became natural to use "밖에" as a whole.
This happens only in casual spoken conversations and usually only for relative location terms. "밖에를", "안에를", "위에를" are often heard but "학교에를", "회사에를", "고향에를" are not.
