Answer:
The correct answer is:
Speaking as loudly as possible.
Explanation:
A participial phrase is the part of a sentence in which the participle of a verb act as the subject of the statement, also having an adjective function in the whole sentence, due to the fact that it qualifies the other action. In this case it is possible to see how the participle of the verb is working as the subject, that is the reason why, it is considered the participle phrase, and it also modifies the second part of the sentence since it gives a description about it.
Some other examples of participle phrases would be:
Walking on the beach is great on vacation time.
Running in the mornings is my favorite activity.
Smiling and waving, she said hello.