If you are given 'a free hand' it means that you are allowed to do as you wish.

It means the Japanese wanted to be able to trade or engage in military activity without interference from other nations.

The Japanese demanded a free hand from the United States in Asia. 这句话的意思是“日本要求美国不要干预它在亚洲的事物。"这里使用的是比喻的意思，指“自由决定权”，通常表达为give someone a free hand的形式， 意思是“让某人自由行事”。 a free hand字面上看就是“自由的手”，如果你的手上没有拿任何东西，那就它就可以称作a free hand。