how long will 350000 dollars last with a 24000 per year draw down and a 8 percent return on the balance?

Answer 1

Forever,

even if you deduct $24K in the beginning, it leaves $326,000 which will return a simple 8% return on the balance of $26,080. That means your balance will continually be growing

Answer 2

Forever, since it would increase each year. After the first year for example, your return of 8% on the remaining 326,000 would be a little over $26,000, more than enough to cover the next year's 24K withdrawal, etc ad infinitum.