高一英语一道选择题

apologize for+名词性成分，动词要变成动名词形式，所以排除B，动名词否定式not 要在动名词前面
ted为他没能通知我计划有变而道歉

apologize for+名词短语
his not being able=名词短语

I must apologize for not being able to meet you. 名词短语=not being able to meet you.

我因为没能接你而向你道歉

I must apologize for my discourtesy in arriving late. 名词短语=my discourtesy in arriving late
我要为迟到失礼而道歉。

You should have the decency to apologize for what you did.
你应该讲点礼貌，为你所做的事道歉。名词短语=宾语从句(介词宾语)=what you did.

I apologize for encroaching upon your valuable time, but I should appreciate you advice in an important matter. 名词短语=encroaching upon your valuable time我很抱歉占用您宝贵的时间，但有一件重要事情我希望能得到您的建议。

C、his not being able
这是动名词的复合结构 的否定形式 作介词宾语
A 否定形式不对 否定词应放在 动名词前面
B 不是动名词 故 错

A 否定的not放在动词的前面。
B him是he的宾语形式。

C,being 是动名词，相当于名词的用法