Adjective closest to the noun
To expand upon the last paragraph in gotube's answer, it is important to remember that the adjective closest to the noun is the most important (given a particular context), and that importance decreases, the further that the adjective is placed away from the noun.
Therefore, in the OP's context:
- the main topic is about companies in Japan, and;
- the second most important part of the conversation is about those companies in Japan which are huge.
Thus, the overall topic of the conversation is
huge Japanese comapnies
Therefore, if a participant in the conversation wants to bring up the fact that there is a new example of such companies, then the "new" needs to be tacked on to the start (because it is of the least importance, given the context of the preceding conversation):
new huge Japanese company.
Examples for alternate main topics
Taking this even further, if the conversation was about huge companies around the world, and the new huge company was opening in Japan, then (while it does sound strange) it would make sense to say:
A new Japanese huge company.
Likewise, if the conversation was about new companies opening around the world, and one such company was opening in Japan, then the following would make sense:
A Japanese new company.
These are obviously edge cases, and really do not sound natural - because usually, in most natural conversations, the geographical location of the company is the most important aspect of the company, and not its newness or size.
Another example would be in a theoretical (not to mention bizarre) conversation about new doors, it would be logical to say
I have a green new door.
However, in normal conversation (and not one specifically about new doors being fitted), the above would sound strange, and it would be more natural to say
I have a new green door
Having said all of that, I would add that if I was reading the newspaper and I saw that Elon Musk has opened a "giga-factory" in Kyoto, I would most likely say to my friends,
A huge new Japanese factory has just been opened!
It just sounds the most natural way of saying it, if it was a non-sequitur statement, i.e. no one had previously been talking about factories, be that Japanese, huge or otherwise.
Why does it seem the most natural? Because, in order of importance: the factory is in Japan; it is new, and; it just so happens to be huge.
Therefore, as no particular context was given in your worksheet, I would say that you worksheet is incorrect.