Translation:Do not let the child play with the knife.
"kid" is a bit less formal than "child", although it can also be translated as "enfant", it could also be translated with the more familiar "gamin(e)" (although the difference with "enfant" is a bit stronger than between "kid" and "child").
Nevertheless, I wouldn't personally count it as a wrong translation, especially without context.
Because we use the infinitive form for this sentence to make sense.
For example you would not say : "Do not let the child plays with the knife." (even though it should, because "the child" is the third person singular) because the verb "play" is in the infinitive form, otherwise the sentence makes no sense.
It looks like there are two possible (literal) English translations- "Do not let the child play with the knife." and "Do not leave the child to play with the knife.". Obviously these mean quite different things in English- the first is about allowing/permitting something, the other is about physically removing yourself from the situation.
Assuming the former is definitely correct (as it's the suggested answer)- is the second one valid too? It was accepted, but as it's a literal translation that doesn't always mean it makes sense as a French sentence...
I wouldn't really say that the second translation is correct, although it could be debated that removing yourself from a situation with a child is just like allowing or at least not preventing the child to do something.
If I wanted to use the second meaning less ambiguously, I would use something like "Ne laissez pas l'enfant jouer seul avec le couteau." or "Ne laissez pas l'enfant seul avec le couteau.".