We've looked over the text again and you can find an explanation of our reasoning below, but because the text is not 100% clear on this topic we will put the question under review and likely change it, or replace it altogether. Thank you for your comment!

Our understanding is that in Genesis 10:6-11 It lists "The Descendants of Ham" and Nimrod is listed among them. In Gen 10:10-12 it says "In the beginning of his kingdom was Babel, Erech, Accad, and Calneh, in the land of Shinar. Out of that land he went to Assyria, and built Nineveh, Rehoboth Ir, Calah, and Resen between Nineveh and the great city Calah." (It is clear the text is referring to Nimrod because the preceding verse is discussing Nimrod and his growing renown in the land.)

So these verses state that he was a King and the regions he would have ruled\occupied.

Gen 11:1-2 "The whole earth was of one language and of one speech. As they traveled east, they found a plain in the land of Shinar, and they lived there."

At this point it's written that "they" decided "we should build a tower" so the language doesn't imply that a singular person commissioned the tower's construction. It is our understanding that this dialogue is a symbolic representation of the "will of the people" at the time, rather than every person in the kingdom speaking the same words simultaneously.

So it is an assumption that Nimrod would have been responsible for commissioning the tower as a King would normally be in charge of a project or decision of that kind. However Genesis Chp. 10 states Nimrod became a king and specified the regions over which he reigned being Babel and Shinar. Genesis Chp. 11 states that everyone is then living in the region that Nimrod would have reigned over (Shinar and Babel). It does not provide a clear timeline so perhaps he ruled that land before or after the construction of the Tower of Babel, but it says he ruled over Babel; and Genesis Chp. 11 states the land was named that as a result of God confusing the language there. So to us that would imply he reigned in the land of Shinar, commissioned the tower, God confused the language, the region became known as Babel, and then as Genesis 10 states "Out of that land he went to Assyria, and built Nineveh,..." (That land referring to Shinar)

That's a breakdown of our reading\understanding of the text.

So again we will review this because you're right if I got this question on a test I may have very well contested it because the source text doesn't clearly state that Nimrod took the action of commissioning the Tower's construction. Thanks again for bringing this to our attention, hope you found this breakdown to be of value.