A person walks outside carrying a bag, while a young girl in pink walks behind her.
A person carrying a bag with a girl behind her
A person walks outside carrying a bag, while a young girl in pink walks behind her IS THE SAME AS A person carrying a bag with a girl behind her
'with a girl behind her' is a simpler rephrasing of ' a young girl in pink walks behind her.'
If a person walks carrying a bag while a girl walks behind her, then that person carrying a bag has (is with) a girl behind her.