Answer:
The correct answer option is 'participial phrase'.
Explanation:
We are given the following sentence:
'The old man sat at the window, remembering the days when he would have gone outdoors'.
Here, the italicized words are an example of participial phrase.
A phrase which looks like a verb but actually functions as an adjective while modifying a noun in the same sentence is called a participial phrase.
So in this sentence, 'remembering' is the present participle and 'remembering the days' is the participial phrase. The participial phrase modifies 'he'.