Assuming you're using the stock e-mail app:
With the app open, long-press each e-mail until you see a check mark to the left of each e-mail, then tap the trash can at the top of the screen.
Great question, MangiaMama, we know how important it must be to be able to delete all of your emails at once. So let me start off by asking you, what is the make and model of your device? Also, what email app are you using?
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