The scene where Andy Dufresne told the warden he'd never tell anyone about cooking his books

When Andy's trying to get the warden to let Tommy tell them he's innocent

https://m.youtube.com/watch?v=_IrCgt-Bt1I&t=3m53s#

It's this scene (around the 3:55 mark in this clip):

https://youtu.be/_IrCgt-Bt1I?t=3m55s