Here's why:
* "Every discussion forum initial response prompt and peer" is a singular noun phrase, referring to each individual prompt and each individual peer.
* "their" is a plural pronoun.
To correct it, you have two options:
Option 1: Use a singular pronoun
> Every discussion forum initial response prompt and peer will have its own guidelines for required information.
Option 2: Use a plural pronoun and change the noun phrase to be plural
> All discussion forum initial response prompts and peers will have their own guidelines for required information.
Choose the option that best fits the intended meaning and the tone of your writing.