Fill in the blanks with the most appropriate option:-

He asked me …………I had gone there or not.

whether

The correct option to fill in the blanks is whether.

The sentence is about someone asking the speaker if they had gone somewhere. The word "whether" is used to introduce a question about a choice or possibility. It is the most appropriate word to use in this context, as it describes the speaker's uncertainty about whether or not the speaker had gone somewhere.

The other options are not as appropriate:

• That is used to introduce a statement or explanation. It is not as appropriate as "whether", as it does not convey the same sense of uncertainty or doubt.
• What is used to introduce a question about a fact or thing. It is not as appropriate as "whether", as it does not convey the same sense of choice or possibility.
• Why is used to introduce a question about a reason or cause. It is not as appropriate as "whether", as it does not convey the same sense of choice or possibility.