Explanation:

To determine the correct answer, we need to understand the concept of degree of adverbs.

Adverbs are words that modify verbs, adjectives, or other adverbs. They often describe how an action is performed or the degree of an adjective or adverb. Adverbs can be modified to show different degrees: positive, comparative, and superlative.

Comparative adverbs are used to compare two actions or qualities. They are formed by adding -er to the base form of the adverb or by using "more" before the adverb. Superlative adverbs are used to compare three or more actions or qualities. They are formed by adding -est to the base form of the adverb or by using "most" before the adverb.

In this sentence, we are comparing the running speed of Lance and Matt. Lance runs fast, but the question is asking for the appropriate adverb to complete the sentence. Let's analyze the options:

a) fastest - This is the superlative form of the adverb "fast." It is used to compare three or more actions or qualities. However, in this sentence, we are only comparing two individuals, so the superlative form is not appropriate.

b) fast - This is the positive form of the adverb "fast." It simply describes the speed of Matt's running. While it is grammatically correct, it does not convey the comparison between Lance and Matt.

c) faster - This is the comparative form of the adverb "fast." It is used to compare two actions or qualities. In this sentence, we are comparing the running speed of Lance and Matt, so the comparative form is appropriate. Therefore, option 'C' is the correct answer.

d) more fast - This is an incorrect form. While "more" can be used to form the comparative degree of adjectives, it is not used with adverbs. The correct form is "faster."

To summarize, in the sentence "Lance runs fast but Matt runs ______," the correct adverb to complete the sentence is "faster" (option 'C').