Translation:He will go to Japan in two weeks.
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."
Not really. It depends on context.
- If you are talking about two weeks from now you would say "in two weeks" but
- if you are talking about two weeks after some point in time in the future then you would normally say "two weeks after that".
- If you are talking about going after two weeks of some activity then you would say "after two weeks (of that activity)" irrespective of whether the two weeks starts now or in the future.
So my conclusion is your answer using "after two weeks" would only be used if in a previous sentence or the context generally you had already specified the answer to "after two weeks of what?"