I see that you're having a problem printing photos from your iPhone to your AirPrint enabled printer. Instead of immediately printing, you receive a message that it's being prepared. I also see that your significant other isn't having an issue, and I'm happy to help.
If you can‘t print from your Mac or iOS device -- Even though she is able to use AirPrint without a pause, there could be an issue that's only affecting your phone. Follow the steps provided in this article.
If you're still having a problem using AirPrint, please answer the following questions:
- Which iOS is your iPhone 6 currently on? Find the software version on your iPhone, iPad, or iPod
- Are you using iCloud Photo Library to sync your photos between devices, and are you optimizing the storage space for photos on your phone? iCloud Photo Library
- Does this issue occur when you use AirPrint every time, or does it appear to be just your photos?
Let me know how that goes.