Which words are in italics?
Which sentence do you think is correct?
This is to test your knowledge of "adverbs." "Adverbs" are words that are used for the purpose of telling "HOW" an action was done, in what way.
For example, he walked "slowly." HOW did he walk? "Slowly."
She screamed "loudly." Sure she scremed, but HOW did she scream? "Loudly."
Notice that within the word "adverb" you see the word "verb". This is a reminder that adverbs and verbs are related to one another.
Words that end in "ly" and are used to describe HOW an action is done are "adverbs."
Of course, people who are obsessed with grammar aren't satisfied that you learn how most adverbs are used. The want to test you on the exceptions to the rule. Sentences "B" and "D" above are exceptions to the rule because, in cases where the verb describes a perception, like "to taste" and "to feel," the "ly" is NOT used on the end of the adverb. People feel sad. They don't feel "sadly," probably because there's not much physical action involved in feeling, and so "feel" is hardly a verb at all.
Anyway, that's the distinction that they are testing you about, and maybe the only way to get these questions right is (a) to understand the explanation above and (b) to memorize the verbs that do not take "ly" adverbs, e.g. "feel," "taste," look," "smell," "sound"... What they all have in common is that they're about the five senses, so don't use a "ly" adverb to describe how someone uses their five senses.
"He looked longingly" is correct.
"He looked badly" is not correct. The first is about an action while the second is about an appearance, which doesn't involve much action. When the verb involves a sense appearance, don't use an adverb ending with "ly."
Likewise, if you "feel bad" then you feel "down" and sad.
But, if you feel "badly," then you are bad at feeling. You are bad at doing the act of feeling. If you are bad at doing the act of feeling, then you don't feel badly; you don't feel anything at all.