Exact wording of the problem implies you're getting 6% per day:
P = Po*1.06^t
2Po = Po*1.06^t
2 = 1.06^t
ln(2) = ln(1.06^t)
ln(2) = t*ln(1.06)
t = ln(2)/ln(1.06)
t = about 11.89566
Answer: In about 12 days
If the problem is asking about an annual interest rate of 6%, compounded daily, then:
P = Po*(1+0.06/365)^t
2Po = Po*(1+0.06/365)^t
2 = (1+0.06/365)^t
2 = (1+0.00016438356)^t
2 = (1.00016438356)^t
ln(2) = ln(1.00016438356^t)
ln(2) = t*ln(1.00016438356)
t = ln(2) / ln(1.00016438356)
t = 4216.9919 (days)
4216/365 = 11.5534 (years)
11*365 = 4015
4216-4015 = 201
Answer: In about 11 years 201 days.