Adverb Formation:
An adverb is a word that modifies a verb, adjective, or another adverb. Adverbs often end in -ly, but not always. To form an adverb from an adjective, we generally add -ly to the end of the adjective. However, there are some exceptions to this rule.

Forming the Adverb of 'Loud':
The adjective 'loud' describes a sound that is strong and powerful. To form the adverb of 'loud', we need to add the suffix -ly, resulting in 'loudly'.

Different Options:
Let's analyze the given options to understand why 'loudly' is the correct adverb form of 'loud':

a) 'Louder' is a comparative form of the adjective 'loud'. It is used to compare two things and does not function as an adverb.

b) 'Loudfully' is not a recognized English word. The correct adverb form of 'loud' is 'loudly'.

c) 'Loudly' is the correct adverb form of 'loud'. It describes the manner in which something is done or the intensity of a sound.

d) 'Loudily' is not a recognized English word. The correct adverb form of 'loud' is 'loudly'.

Therefore, the correct adverb form of 'loud' is 'loudly' (option C).

Summary:
The adverb form of the adjective 'loud' is 'loudly'. It is formed by adding the suffix -ly to the end of the adjective. The other options provided are not correct adverb forms of 'loud'.