O que significa An 18-year-old who is fresh from “a million” foster placements, living in a kind of halfway house for people transitioning out of care. ?

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"a million" is just an exaggeration for "very many".
Transitioning out of care - Children who cannot live with their parent/parents for some reason (physical or mental problems with the child or the parents, including drug addiction and crime) are often "put into care" where they are placed in a special home and provided for by the government. Once they reach adulthood however they must move out of such a home. It is almost impossible for such young adults to just be thrown into adult society and so there are often places set up which are less like a care home and more like semi-independent living so thay can gradually change to (transition to) normal adult life.