First, welcome to the forum! If you are sincere in looking for perspective and advice, you'll very likely find it here.
Second, and not to set the wrong tone, but could you edit your post to include some punctuation? That would make it easier to read and understand, and it would also give more of impression that you are serious in asking for help.
Third, could you provide some more background, a few details on how all this unfolded, what was actually said, when and to whom?
At first flush, I'd say the order of things matters a lot: asking for an open relationship after cheating is certainly a problem!
True poly relationships - and you can find out a lot on this site about what makes a poly relationship different from an open relationship - are based on trust, honesty, and consent.
If your girlfriend is really serious about an open relationship, and if she really has already cheated with this other guy, she needs to know she has a lot of work to do to restore trust.
Also, if she's serious about wanting an open relationship, maybe you could encourage her to check out this forum, maybe even sign up and offer her own account of things.
