The correct answer is:
Waving to the crowd, Queen Elizabeth rode in a carriage drawn by two Windsor Greys.
A participial phrase is a combination of words consisting of a participle and the modifier or nouns, pronouns and noun phrases that operate as direct objects, indirect objects, or complements of the action or state formulated in the participle. To avoid confusion, a participial phrase must be placed as close as possible to the noun it modifies and the noun should be explicitly stated.