I want to start reading the manga Naruto Shippuden, but I would rather start reading from the last episode that was aired (currently episode 413). Do you know which chapter that episode (episode 413) would be?
Naruto: Shippuden episode 413, titled Hopes Entrusted to the Future, is a filler episode. The entire arc, In Naruto's Footsteps: The Friends' Paths, is a filler arc. Meaning, none of the episodes from the arc has a manga equivalent and is anime exclusive.
However, if you want to check the manga equivalent of an episode from the main arc, you can get the episode details from Naruto Wikia.