The verb عاد (ʿāda) is a hollow verb (فعل أجوف) from the root ع-و-د. When this verb carries the meaning "to return" (الرجوع), its verbal noun (مصدر) is عودة (ʿawda). This is a standard مصدر pattern for hollow verbs of this type: the middle weak letter (واو) appears in the noun form, and the تاء مربوطة is added at the end.
It is important to distinguish between the different meanings the root ع-و-د can carry, because each meaning has its own مصدر. When عاد means "to return," the مصدر is عودة. When عاد means "to visit a sick person" (عاد المريضَ), the مصدر is عيادة. In this question, the context points to the general meaning of returning, making عودة the correct answer.
The remaining options do not fit. عود is a noun meaning "stick" or "lute" (the musical instrument), not a مصدر of عاد in the sense of returning. عادة means "habit" or "custom" and is a noun in its own right, not the verbal noun derived from عاد meaning "to return." Recognising that a single Arabic root can yield different مصادر depending on the verb's meaning is a key skill in صرف (morphology).
