12. public schools in the uk are for.. a) 11-12 year-olds b) 4-5 year-olds c) 7-8 year-olds d) any school age

В источниках, в инете пишут возраст 13-18. У тебя такого варианта нет. Я нашла статью об этом, прочитай ее

public school  particularly in England, which cater primarily for children aged between 13 and 18.
Differences between British and American English: public schoolIn the UK, a public school is a private institution for young people between the ages of 13 and 18 whose parents pay for their education. The students often live at the school during the school year. American speakers usually refer to this as a private school. In the US, public school refers to a school that is paid for from taxes and provides free education to local children between the ages of about five and 18. This is called a state school in the UK.