Historians do not typically say that there were six foreign powers that fought against the rebels in the Boxer Rebellion.  Instead, they typically say there were eight.  For example, the history-fact-finder link below says

The Boxer Rebellion was an uprising that took place in China in 1900. It was crushed by the combined forces of eight foreign countries...

It may be that your textbook feels that the contributions of two of the foreign powers were not significant enough to be worth mentioning.  You may want to check to be sure.

The eight nations that are generally credited with helping to put down the Boxer Rebellion are:

• Japan
• Russia
• Great Britain
• France
• United States
• Germany
• Italy
• Austria-Hungary

I would argue that the last two of the countries mentioned above did the least to help put down the rebellion.  Therefore, if I were to limit my response to six countries, I would use the top six on the list above.