This is the 5534th most frequent Japanese word.
かいがいしく
Diligently; industriously; in a hardworking and devoted manner.
Here, かいがいしく is used to denote someone's diligent and proactive attitude in accomplishing a task.
彼は会議の準備をかいがいしく進めています。
He is diligently preparing for the meeting.
In this context, かいがいしく emphasizes the meticulous effort and care the grandmother shows in her gardening activities.
祖母は庭の手入れをかいがいしくしています。
My grandmother is diligently taking care of the garden.
The usage of かいがいしく here highlights the person's dedication and earnestness in their work.