Yes, take out a ball from the box with a red label and a white label. (1) If it is white, there are two white balls in this box. Then, because all the labels are wrong, it can be judged that there can only be one red and one white in the box with the red label and only two reds in the box with the white label.

(2) If the red balls are taken out for the first time, it means that there are two red balls in the box marked as one red and one white, only one red and one white in the box marked as two white, and two white labels in the box marked as two red.