Translation:He will go to Japan in two weeks.
"after two weeks he will go to japan" was rejected but I think should be accepted
I'm afraid "after two weeks" is not how we express "two weeks from now" in English.
It's just the way it's phrased in Chinese. "After two weeks (have passed) " and "in two weeks" mean pretty much the same thing in English too.
Unfortunately if you are going to learn Chinese via English you will have to be comfortable with how things like this are actually phrased in English.
I know this is a very common way that non-native English speakers say it while they're still learning.
I have translated it like so: "He will go to Japan after two weeks." Even though I think that "in two weeks" sounds better, nevertheless my translation should be accepted. Do the native English speakers agree?
后 translates to "after," but that does not mean that 两个星期后 translates to "after two weeks."
In this case, I personally do not think that "after two weeks" is correct. (I'm a native American English speaker.) To me, "He will go to Japan after two weeks," sounds like an incomplete sentence that, even when completed, would mean something different than "He will go to Japan in two weeks."
"In two weeks" means two weeks from now. "After two weeks" means two weeks after SOMETHING, but this sentence does not include the something and therefore sounds incomplete to me.
He will go to Japan after two weeks OF WHAT? Perhaps: "He will go to Japan after two weeks of working," or "He will go to Japan after two weeks of studying," but not just "He will go to Japan after two weeks." Perhaps "He began his trip in China, then he went to Japan after two weeks." (These are examples of how "after two weeks" could be used in an English sentence. They are not translations of the Chinese sentence in this exercise.)
As far as I can tell, the Chinese sentence indicates two weeks from now, which should be expressed as "in two weeks."