[译] 我因弄错了这件事而向你道歉。
[误] I apologize to you to be mistaken about it.

[正] I apologize to you for my being mistaken about it.
[注] apologize 后不接动词不定式，表示“为做某事而道歉”时，应该说 apologize for doing sth.。同样，表示“为某事而道歉”时，应该是 apologize for sth.