If you have already created a custom domain for the lightning modules, and now you are working on the Apex Web Services module in Apex Integration Services on trailhead, you might wonder how you are supposed to find your instance.
curl https://instance.salesforce.com/services/apexrest/Cases/<Record_ID> -H 'Authorization: Bearer<your_session_id>' -H 'X-PrettyPrint:1'
and enter what you have left into the lookup box, and click find. Viola! You have your instance. Now finish updating your cURL text and continue on your trail.