I will try with all my might to successfully accomplish this important task.
You volunteered for such a great duty, eh?
Frodo, of the Lord of the Rings, was given the most important task and he did it all without putting on shoes.
A big duty is a great duty. It can also be an important task. Think about some kind of big duty you have. Then, think about what an important task it is too. Feel proud of your important task.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.