Adjectives are the words that define/explain nouns or pronouns. For example: Roshni is pretty. Here, 'Roshni' is the noun and 'pretty' explains how she is, hence 'pretty' is the adjective.

Adverbs are the words that describe action words (verbs). For example: Ram fought bravely. Here, 'Ram' is the noun and 'fought is the verb. 'Bravely' describes how he fought, hence it is the adverb.

NOTE: The first sentence requires an adverb to describe how cold the weather is, and the second sentence requires an adjective to describe the weather.

Option A - 'Awful' is an adjective and hence can't be used with the first sentence. 'Awfully' is an adverb and hence it can't be used with the second sentence. Thus option A is incorrect.

Option C - 'Awful' is an adjective and hence it can't be used with both the sentences. Thus option C is incorrect.

Option D - 'Awfully' is an adverb and hence it can't be used with both the sentences. Thus option D is incorrect.

Option B - 'Awfully' is an adverb which can be used to describe how cold the weather is. 'Awful' is an adjective which can be used to describe the weather. Hence, option B is the correct answer.

'The weather is awfully cold today. The weather is awful.'