How do I purchase games for free

How can I make free purchases

It is not possible.

If you want to purchases or update / download apps, including free apps, you need to update your payment method or add a new one. 

See also the following Apple articles:

Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)

Add money to your Apple ID balance

Add money to your Apple Account balance – Apple Support (UK)

If you update your payment method or add funds to your Apple ID balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.

Click here for more support and assistance.