"연구원은 남자가 한국어를 못한다고 추측했어요."
Translation:The researcher guessed that the man could not speak Korean.
I can try
연구원은 남자가 한국어를 못한다고 추측했어요
연구원은 = the researcher 남자가 = the man 한국어를 = (in) korean 못한다고 = cannot do (with ㄴ다고 meaning a quote of some sort) 추측했어요 = assumed/guessed
The researcher / assumed (that) / the man / cannot (couldn't) speak korean
The researcher assumed the man cannot speak korean
I spent some time picking apart each word, like @Shlomo_, looking for something that implies speak directly, too, and your explanation, @Iron_Venema, makes sense. To help make it stick in my head, for "한국어를 못한다고", if you can't do the Korean language, they mean you can't speak it. So, "한국어를" isn't just a language, it's the skill of being able to use the Korean language? Even if it doesn't make sense to anyone else, it makes sense to me.