The correct option is A Shouting with happiness
A participle is that form of the verb which partakes of the nature both of a Verb and of an Adjective.
A participle phrase will begin with a present or past participle. If the participle is present, it will dependably end in ing. Likewise a regular past participle will end in a consistent ed.
Since, all phrases require two or more words, a participle phrase will often include objects and/or modifiers that complete the thought.
Participle phrases always function as adjectives,adding description to the sentence.
In this case,
Option A is correct. The present participle phrase, 'Shouting with happiness' describes the noun 'William'.
Option B is incorrect as 'celebrated' is a verb.
Options C and D are incorrect as they don't contain any participle in them.