If an inmate was sentenced to 78 months how much time does he have to serve before he can get out and does the release date on the BOP website before or after good time RDAP etc time

The BOP release date is accurate. Once the inmate gets approved for RDAP, it will change the release date. It takes about 2-3 months for the change to appear on their website. The good time credit of 15% is included in the release date and as long as the inmate steers clear of incident reports, that amount will stay with them to the door. 

On 78 months, with good time there are 66.3 months to serve. If they get RDAP, that takes twelve months off to make it 54.3. They also get an automatic six months of halfway house which reduces the time inside down to 48.3 months to release (into the halfway house). Almost exactly four years down from six and a half years, that is the best deal an inmate can get unless they cooperate and get a snitch reduction. 

I had a 96 month sentence, had a clean record throughout, did RDAP and got out in 66 months.