"He couldn’t finish his homework owing to his illness."

The correct answer is Option (1) → Adverb of Reason

An adverb is a word that tells how, when, where or how much something happens. It can also describe an adjective or another adverb, for example she sings sweetly, very hot.

Owing to means because of. So “owing to his illness” tells why he could not finish his homework. A group of words that does the work of an adverb is an adverb phrase.

Option	What it tells	Example
(1) Adverb of Reason (answer)	why something happens: this phrase gives a reason	The school stayed shut owing to heavy rain.
(2) Adverb of Time	when something happens: the phrase gives a cause, not a time	I finished my homework yesterday.
(3) Adverb of Place	where something happens: illness is not a place	The children are playing outside.
(4) Adverb of Manner	how an action is done: the phrase tells why he could not do his homework, not how	She folded the clothes carefully.