我不仅擅长汉语和英语，还具备良好的跨文化交际能力。A Not only I am good at Chinese and English, but also have I cross-cultural communication skills.B Not only do I good at Chinese and English, but also I have cross-cultural communication skills.C Not only I am good at Chinese and English, but also have I cross-cultural communication skills.D Not only am I good at Chinese and English, but also I have cross-cultural communication skills.

这道题考查的是英语中 Not only... but also...（不仅……而且……）句型的倒装规则。

1. 分析核心语法点：

• 句型结构：当 Not only... but also... 连接两个分句，并且 Not only 置于句首时，为了强调，Not only 引导的前半句需要使用部分倒装（即把助动词、情态动词或 be 动词提到主语前面）。
• 后半句语序：but also 引导的后半句则保持正常语序（主语 + 谓语），不需要倒装。

2. 分析句意与动词搭配：

• “擅长汉语和英语”：英文表达为 be good at Chinese and English。主语是“我”（I），所以对应的系动词是 am。
• “具备……跨文化交际能力”：英文表达为 have cross-cultural communication skills。

3. 逐项分析选项：

• A. Not only I am good at Chinese and English, but also have I cross-cultural communication skills.

  • 前半句 Not only I am... 没有进行倒装，错误。
  • 后半句 but also have I... 进行了倒装，错误（后半句不应倒装）。

• B. Not only do I good at Chinese and English, but also I have cross-cultural communication skills.

  • 前半句使用了助动词 do 进行倒装（do I good at）。因为 be good at 是系表结构，不能借助实义动词的助动词 do 来倒装，而应该直接把 be 动词 am 提前。所以前半句错误。
  • 后半句语序正确。

• C. Not only I am good at Chinese and English, but also have I cross-cultural communication skills.

  • 此选项与 A 完全相同，前半句未倒装，后半句错误倒装，均不符合规则。

• D. Not only am I good at Chinese and English, but also I have cross-cultural communication skills.

  • 前半句 Not only am I... 将 be 动词 am 提前到了主语 I 之前，实现了正确的部分倒装。
  • 后半句 but also I have... 保持了正常的主谓顺序，完全符合语法规则。

结论：
经过推理分析，只有选项 D 完全符合 Not only... but also... 的倒装语法规则和动词搭配。

正确答案是：D