How do I cancel a purchase?

What kind of purchase? You cannot cancel a purchase but you can request a refund. You get 14 days for most Apple hardware. If you're asking about an app or media purchase, here's how to request an app or media refund from Apple (From: Request a refund for apps or content that you bought from Apple - Apple Support - see the article for more detail.) If you bought this in the EU from a third party, see: About purchases not billed through the App Store or the App Store’s In-App Purchase system - Apple Support instead.

1. Sign in to https://reportaproblem.apple.com

2. Tap or click "I'd like to," then choose "Request a refund."

3. Choose the reason why you want a refund, then choose Next.

4. Choose the app, subscription, or other item, then choose Submit.

If you were charged for a subscription that you no longer want, you can also cancel the subscription using the directions in this article --> If you want to cancel a subscription from Apple - Apple Support

Read this support article for information about how long it takes to receive a refund (if you are granted one), and how to check the status of a refund for apps or content that you bought from Apple --> Check the status of a refund for apps or content that you bought from Apple - Apple Support

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Purchases are processed more or less instantaneously, so there is not really a way to cancel them. If there is a reason, you can try requesting a refund: Request a refund for apps or content that you bought from Apple - Apple Support