To solve this problem, we need to identify the method of vegetative propagation in ginger.$\newline$Let's analyze the options:$\newline \bullet$Option 1: Rhizome - A rhizome is a horizontal underground stem that often sends out roots and shoots from its nodes.$\newline$ - Ginger propagates vegetatively through rhizomes, which store nutrients and help the plant survive adverse conditions.$\newline \bullet$Option 2: Offsets - Offsets are small, complete daughter plants that grow from the base of the parent plant.$\newline$ - This method is common in plants like succulents and not applicable to ginger.$\newline \bullet$Option 3: Bulbils - Bulbils are small bulbs that form in the place of flowers or in leaf axils.$\newline$ - This method is seen in plants like garlic and lilies, not ginger.$\newline \bullet$Option 4: Runners - Runners are horizontal stems that grow above ground and form new plants at their nodes.$\newline$ - This method is typical in plants like strawberries, not ginger.$\newline$Therefore, the correct method of vegetative propagation in ginger is through rhizomes.$\newline$This corresponds to Option 1: Rhizome.