Believe it or not at age 6, here's the kicker though; NEVER make a child under the age of 15 "feel the burn." Taking it to the point where the muscle begins to burn, should only be done at age 15. Even then, at 15, only a moderate burn, and the burning sets taken to progressive intensity to high intensity only by age 18. Now, if its calisthenics, you can train a kid as hard as you want and nothing bad will happen provided they are not overtrained; literally thousands of boys in strength based sports such as American football or Wrestling do cals and they grow tall just fine. However high intensity weight training, it has made more than one dude with a tall father shorter than he should be.
Weight training is fine for kids but NEVER take it to the burn; you want to use light weights, and take it JUST to the point of fatigue, the half way point between the resting phase of the muscle and the burning point, that is, to the point where blood flow to the muscle is felt but NEVER tear up the muscle fibers. NEVER, EVER, force a child to "feel the burn" while lifting, its dangerous, very dangerous. Any strength coach will confirm what I just said here.
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You can lift wights at any age you want in private, but in places like gyms and sports centers expert trainers say you should be 15-16+. Although a 12 year old could lift weights, their arms and bodies aren't fully grown. Although they look alright on the out side they could cause damage on the inside.
I would wait until your in junior high or 7th grade before I started to lift heavy as your muscles just aren't ready before that.