In Magento, you can set a 10% discount for a specific customer by creating a shopping cart price rule. Here are the steps to do so:
Log in to the Magento admin panel
Go to Promotions > Shopping Cart Price Rules
Click on the “Add New Rule” button
In the “Rule Information” section, give the rule a name, set the status to “Active”, and choose a “Customer Group” to which the discount will apply.
In the “Conditions” section, set the rule to “Apply the rule only to cart items matching the following conditions” and select the “Quantity in cart” and “is” options and set it to 1
In the “Actions” section, set the “Apply” option to “Percent of product price discount” and set the discount amount to 10.
Click on the “Save Rule” button
Once you’ve saved the rule, the 10% discount will be automatically applied to the cart when a customer from the selected group checks out.