There are 12 cookies in 1 dozen, so in the morning, she sold 12 x 3 dozen = <<12*3=36>>36 cookies.
Throughout the day, she sold 36 cookies in the morning + 57 cookies at lunch + 16 cookies in the afternoon = <<36+57+16=109>>109 cookies.
She started with 120 cookies – 109 cookies sold = <<120-109=11>>11 cookies to take home.
#### 11