Slowly is the correct answer because it is an adverb that describes the way in which the action of eating is performed. In this sentence, we are describing how the sister eats, not comparing her eating speed to someone or something else.

- adverbs modify verbs, adjectives, or other adverbs to provide more information about how, when, where, or to what extent an action is performed. In this case, slowly modifies the verb "eats" to indicate that the sister eats in a slow manner.

Let's break down the options and explain why they are incorrect:

a) Slow: Slow is an adjective, not an adverb. It describes the sister, not the action of eating. Therefore, it does not fit in the sentence.

b) Slower: Slower is a comparative form of the adjective slow. It is used to compare the speed of eating to someone or something else. However, in this sentence, we are not comparing the sister's eating speed to another entity. Therefore, slower is not the correct choice.

c) Slowest: Slowest is the superlative form of the adjective slow. It is used to compare the speed of eating to more than two entities. Since we are only talking about the sister's eating speed, the superlative form is not appropriate here.

d) Slowly: Slowly is an adverb that describes the action of eating. It provides more information about how the sister eats. This is the correct choice because it matches the meaning and grammar of the sentence.

Therefore, the correct answer is option 'D' slowly.