Set up the formula to find the balance after 8 years for a total of $\$ 12,000$ invested at an annual interest rate of $9 \%$ compounded daily.

Step 1 ：Given that the principal amount (P) is $12,000, the annual interest rate (r) is 9% or 0.09 in decimal, the number of times that interest is compounded per year (n) is 365 (since it's compounded daily), and the time the money is invested for in years (t) is 8 years.

Step 2 ：We can use the formula for compound interest to find the balance after 8 years. The formula is given by: \(A = P (1 + \frac{r}{n})^{nt}\), where A is the amount of money accumulated after n years, including interest.

Step 3 ：Substitute the given values into the formula: \(A = 12000 (1 + \frac{0.09}{365})^{365 \times 8}\)

Step 4 ：Solving the above expression, we get \(A = 24651.01059098449\)

Step 5 ：Rounding to the nearest cent, the balance after 8 years for a total of $12,000 invested at an annual interest rate of 9% compounded daily is approximately \(\boxed{\$ 24,651.01}\)