This is the 299th most frequent Hungarian word.
könnyen
Easily.
The word 'könnyen' here is used as an adverb to describe that the task was completed without difficulty.
Könnyen elvégezte a feladatot.
He/She easily completed the task.
In this sentence, 'könnyen' functions as an adverb modifying the verb 'lose', indicating the ease with which someone might lose their patience.
Ne veszítsd könnyen a türelmed!
Don't lose your patience easily!
Here, 'könnyen' again acts as an adverb, describing the effortless manner of the bird's action of flying over the river.