Thank you so much for reaching out to our network and sharing your concerns.
If the payment was made through a third-party gateway, like PayPal for example, then it's possible that you will find the order in your Admin > Orders > Abandoned Checkouts. Sometimes what can happen is that when being re-directed back to Shopify's checkout after successful payment there is some sort of interruption or delay. That means the payment goes through, but the order is not created on Shopify's end.
Since this does not happen often, it's also possible there is another explanation. To ensure it was a successful payment and not just an attempt or hold, have your customer provide you with proof of their banking statement so you can narrow down the charge on your end.
Our Support team would be glad to help you do this. When you access the bot chatbox, simply type in "advisor" and you will be re-directed to live support.
Olivia | Social Care @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog