In the sentence “determining the reason for the great wall’s construction is not easy,” the phrase “determining the reason” is a phrase.

participial

adverbial

gerund

prepositional

The correct answer is C. gerund phrase. Although gerunds and participles look the same (the both take the same form: verb + ing), there is a crucial difference between them - gerunds are only used as nouns, whereas participles can be used as parts of verbs, or as adverbials. Having this in mind, you can see that determining the reason is the subject of this sentence, which also means that it has to be a noun, which means that gerund is the only option which fits this description. A prepositional phrase would start with a preposition, which is not the case here.