Queensland and Australian Capital Territory leaders are unlikely to volunteer to increase how many returned Australians they take into hotel quarantine.

此句为语法错误。increase 可以接名词或代词作宾语，但不可以接 how many 引导的从句。原句想表达“数量”，结果误用了 how many 代替 the number of。

修改如下：

Queensland and Australian Capital Territory leaders are unlikely to volunteer to increase the number of returned Australians they take into hotel quarantine.

【注意】increase 不同于 know，可以接名词或从句作宾语。例如：

I know how many students there are in your school. =

I know the number of students there are in your school.