how to delete a group text that i started

Are you asking about Messages, Apple's built in messing app? Or are you asking about Messenger, the Facebook app?

Hi, joanie242.

I'm glad you decided to reach out on Apple Support Communities. If I understand correctly, you’re wanting to leave the group chat that you started on your iPhone, and you’d like to know how or are having issues.

If everyone in the group is using iMessages (if the chat is blue), you should be able to tap the top of the conversation and choose “Leave this Conversation”. 

If it’s an SMS group (if the chat is green), you may not be able to keep the messages from coming in because they’re handled differently. You may be able to mute the conversation.

This article explains:

Leave a group text on your iPhone, iPad, or iPod touch

Best Regards.