Which is the correct comparative or superlative adverb?
Of all Kate's fans, her family cheers more loudly or most loudly at games.
When comparing her with one other person (so that two people are being compared), use the -er word or the word "more" with the adjective or adverb.
When comparing her with two or more other people (so that three or more people are being compared), use the -est word or the word "most" with the adjective or adverb.
http://grammar.ccc.commnet.edu/grammar/adjectives.htm
Scroll down to Degrees of Adjectives.
http://www.lousywriter.com/adjectives_comparison.php
http://www.uottawa.ca/academic/arts/writcent/hypergrammar/compsupl.html
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In the given sentence, we are comparing the cheering of Kate's family with all of her fans. Since we are comparing more than two people, we need to use the superlative form. Therefore, the correct word to use in this case is "most loudly." The adverb "louder" would be used if we were comparing only two people.
To understand this concept better, you can refer to the provided grammar resources. You can visit websites such as grammar.ccc.commnet.edu, lousywriter.com, or uottawa.ca to learn more about degrees of adjectives and the comparisons of adverbs. These resources will give you a deeper understanding of when to use comparative (-er) or superlative (-est) forms.