Two dozen is 12*2=<<12*2=24>>24.
Eight less than two dozen bandages is 24-8=<<24-8=16>>16 bandages.
She needed two bandages on her left knee and three bandages on her right knee for a total of 2+3=<<2+3=5>>5 bandages.
Therefore, after Peggy finished putting bandages on her knees there were 16-5=<<16-5=11>>11 bandages remaining in the box.
#### 11