"I'm sorry, this is my fault."
不好意思 is for more trivial things. 对不起 for a slightly more serious apology.
In English, "sorry" can have different meanings depending on how it is said and with what intonation.
They both mean "I'm sorry" but Duolingo has the two mixed up! 对不起 is correct here but Duolingo won't take it (not in the word bank, won't accept it typed).