not making sure your cigarette butts are completely out
careless handling of embers from a bonfire
「火の不始末」は英語で次のような言い方ができます。
ーnot making sure your cigarette butts are completely out
「タバコの火の不始末」
ーcareless handling of embers from a bonfire
「焚き火の火の不始末」
例：
Our neighbour's house caught fire because the husband wasn't careful enough putting out his cigarette butts.
「近所の旦那さんのタバコの火の不始末で、彼の家が火事になった」
ご参考まで！
カナダ 
