Your toothbrush and floss can only reach about 3mm under your gums. Your hygienist can scale deeper than that with some anesthesia and special scalers. Also, you can not remove tarter with a toothbrush/floss. If you have 4-6mm pockets it is very unlikely you can reverse them without some help from the pros!
After the initial deep cleaning she will prob recommend you come in every 3-4 months for maintainance appts until your pockets stay at a healthy 3mm level for a period of time and your homecare is as it should be.
fyi - I'm a dental hygienist.