This is the 4733rd most frequent Russian word.
заданию
"Заданию" means "to the assignment" or "to the task" in English (dative case of "задание").
The word 'заданию' is the dative form of 'задание', indicating the task that we're engaging in.
Мы приступили к новому заданию.
We started working on a new task.
'Заданию' in dative case is used to show the relation of the explanation to the task.
Учитель дал подробное объяснение к заданию.
The teacher gave a detailed explanation related to the task.
'Заданию' indicates the direction of the action towards the task, rendered in dative case.