This is the first relocation of the manufacturing factories since its______29 years ago.
(A) founding
(B) founded
(C) found
(D) founder

Answer: (A)

To me, the word 'foundation' sounds much better in the above sentence and I have learned that nouns are usually modified by adjectives and determiners such as 'its' and gerunds are modified by an adverb.
(ex. We will save money by thoroughly reviewing all recent expenditure.
We need to conduct a thorough review of all recent expenditure. )

How could I better understnad the above question?

. . . the manufacturing factories . . .

The word 'manufacturing' is unnecessary. Even seems a bit silly.Emotion: stick out tongue

My only guess is that "its" refers to a company mentioned in a prior sentence. In which case, "founding" sounds most natural to me. Foundation is a noun, so I do not see how you could properly use that here. Found used with an object, (meaning NOT found as in the past tense of to find), means to set up or establish something.
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I might be confused with the words' meaning....

I thought that the following two phrases have the same meaning. Am I understanding something wrong?

the foundation of the company
the founding of the company
Bn77I thought that the following two phrases have the same meaning. Am I understanding something wrong?the foundation of the companythe founding of the company
"founding" is a verb that means "to begin or create", in this case it refers to the point in time when the company was started.

"foundation" is a noun that means "the structure that supports a building"

You should look these words up in your dictionary. And, yes, you will find a definition that means "the act of founding something" but "foundation" is very rarely used in that sense in modern English and I recommend that you avoid it since you are more likely to cause confusion and misunderstanding than to get your point across.
 Clive's reply was promoted to an answer.
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The word "founding" in this context is a gerund, which is a noun, so the idea that "foundation" can't be properly used here because it's a noun makes no sense. (Also, the possessive "its" you mention must be followed by a noun.) The issue is one of usage, not grammar. "Foundation" is generally used to refer to the base (or basis) of something or a charitable institution. Using it in the current context would be unusual, but not wrong.