Yeah, I think it's "hungrily"
Without having more context about what you are studying, it is difficult for me to answer your question. Adverbs modify a verb, an adjective, or to another adverb. They convey a sense of how, when, where, or why. There is not a word that modifies hungry to convey how, when, where, or why the street urchin was hungry. In other words, there is not adverb of hungry in the sentence. So I am guessing your teacher wants you to change the adjective hungry to an adverb. If you rewrite the sentence as follows:
“The street urchin stared hungrily into the bakery shop window.”
The word “hungrily” modifies the verb “stared” to convey how the street urchin stared. In this new sentence, the word “hungrily” is an adverb. It can be called an adverb “of” (or “to”, or “for”) stared. The word “hungrily” can also be considered to be the adverbial form “of” the adjective “hungry”.
“The street urchin stared hungrily into the bakery shop window.”
The word “hungrily” modifies the verb “stared” to convey how the street urchin stared. In this new sentence, the word “hungrily” is an adverb. It can be called an adverb “of” (or “to”, or “for”) stared. The word “hungrily” can also be considered to be the adverbial form “of” the adjective “hungry”.
The adverb for hungry is "hungrily" as it comes from the adjective "hungry" so the noun is"hunger".