Final answer:
The italicized phrase 'to understand' in the sentence provided is an infinitive phrase, which acts as the direct object of the verb 'tried'.
Step-by-step explanation:
The italicized phrase in the sentence, "I tried and tried to understand the problem," is an infinitive phrase. This phrase functions as a noun, adjective, or an adverb in a sentence. In this case, the infinitive phrase "to understand" acts as the direct object of the verb "tried", which tells what the subject is attempting to do. Hence, it is primarily functioning as a noun.
An infinitive is the base form of a verb preceded by the word to. For example, in a different context, an infinitive phrase can serve as a subject, as in "To understand the problem is the first step." Here, the phrase is the subject of the sentence. Infinitive phrases can also function adverbially, as in "To win, you must play smart," where the phrase modifies the verb "must play" by explaining why.