What does on a milk carton mean?
In a movie, there is a scene where a young girl and a boy have an argument.
They are neighbors.
The girl says, "If you were my brother, I'd put myself up for adoption."
Then, the boy says, "Yeah, I hope your face ends up on a milk carton."

I have two questions;
What does put (oneself) up mean in the context?
And what does someone's face ends up on a milk carton mean?
Is 'on a milk carton' an idiom or something?

Question

What does on a milk carton mean?
In a movie, there is a scene where a young girl and a boy have an argument.
They are neighbors.
The girl says,  "If you were my brother, I'd put myself up for adoption."
Then, the boy says, "Yeah, I hope your face ends up on a milk carton."

I have two questions;
What does put (oneself) up mean in the context?
And what does someone's face ends up on a milk carton mean?
Is 'on a milk carton' an idiom or something?

Answer

I'm not American but as I understand it in the US if a child has been kidnapped or gone missing they sometimes put the face of the child on milk cartons with a helpline number to contact, in case anyone knows anything about the child's disappearance. So the boy is saying he hopes the girl goes missing.

To put someone up for adoption means to make them available for adoption. The girl would make herself available for adoption if the boy were her brother. Said in jest I hope.

Answer

For many years there was a national campaign in the US to find and identify missing or abducted children.  One of the practices was to place a picture and a description of the child and his/her circumstances on milk cartons that millions of people in the country would see in the hopes of locating them.  Therefore, hoping that someone's face "ends up on a milk carton" is saying that they wish that this person were gone...missing or abducted.  It was a funny line in "Honey, I Shrunk the Kids" but, when explained, doesn't seem so funny.