my i phone 6 display has broken

Screen repair is available in some countries by Apple or the provider, check this page: Service Answer Center - iPhone

Screen repair service pricing

Repair and replacement costs depend on your iPhone model and your AppleCare product coverage. Apple will run a diagnostic test to determine whether your iPhone has experienced additional damage. If it has, or if it needs other repairs, you may need to pay an out-of-warranty service fee. Accidental damage isn't covered under the Apple One Year Limited Warranty.

Model	Screen repair cost
iPhone 6	$109
iPhone 6s, iPhone 6 Plus, iPhone 5s, iPhone 5c, iPhone 5	$129
iPhone 6s Plus	$149

Plus a $6.95 shipping fee, if required. Fees are in USD and exclude local tax. Pricing is for service through Apple. The final service fee we charge will be determined during testing. Pricing and terms vary for service through an Apple Authorized Service Provider.

copied from Service Answer Center - iPhone

Find an Apple Store, make a genius bar appointment and they'll charge the fees noted above by Ingo2711.

Keep in mind, if the frame is damaged to the point where a new display cannot properly be seated on the device, you'll have to pay for a whole unit replacement. If you have AppleCare+ you'll pay only the service fee instead of the cost of repair in both cases.

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Good luck!