How long do broken arms with surgery take to heal in 12 year old boy?

Too hard to tell. Unfortunately it is too complex to be able to answer. The healing takes place faster in bones of younger people, especially kids. The reason it becomes hard to give you an answer is because there are many factors including what surgery he had and the reasons he had it. I would suggest talking to the surgeon or asking for a second opinion if you feel the need for another opinion.