How can I approve a Ask to Buy request from children when I do not have an apple device?

You can only use iPhone, iPad, iPod touch, Apple Watch, or Mac to approve or decline a request:

Approve what kids buy with Ask to Buy - Apple Support

For your children to send you a request, you need to be the organizer of their iCloud family. iCloud family can also only be set up using an Apple device.

Are you in an iCloud family together? If so, what device did you use to set up the Family?

Family Sharing, including Ask to Buy, can only be set-up and controlled from an Apple device; these features are not available to non-Apple devices, such as Windows PC and Android.

Comprehensive information can be found within these resources:

Approve what kids buy with Ask to Buy - Apple Support

If Ask to Buy isn't working - Apple Support

Apple for Kids - Official Apple Support

Help your child set up an iPhone, iPad, or iPod touch - Apple Support

Family Sharing and Apple ID for your child – Apple Support

Use parental controls on your child's iPhone, iPad and iPod touch – Apple Support