Hi, I wrote a story in '07 called "Honeymoon" and I would like to know if I can delete that story and re-write it.
If I'm allowed it may or may not happen, but I need help to do it if I'm allowed.
Yep, you simply rewrite it and then resubmit the edited version in the submission form. For your story, in the Title field of the form, you'd put Honeymoon - EDITED in the title field (per the instructions here, in the submissions FAQ). I wouldn't bother going through the process of deleting the story first unless there's some reason you need to take it down between now and the time the edited version is posted, but if you ever do need to delete something, you just replace "EDITED" with "DELETE" and then politely ask for the story to be removed from the site in the notes section.
If you need help reworking your piece, or even just an extra set of eyes to catch any errors you likely missed before you resubmit it, head over to the Editors' Forum and find yourself a good volunteer editor after you've gone over your story with a fine-tooth comb on your own. I believe having a great editor and preferably one or more beta readers (you can ask for beta readers in the Editors' or Story Feedback forum, or even just use friends who are sharp writers and willing to give constructive criticism) is almost always essential to making our work the best it can be. It's definitely worth the extra time and effort to get that help and make changes, especially since you care about your story enough to redo it, you know?