Explanation:

- We are asked to find the principal amount (Rsx) that amounts to Rs12,777.60 after 2 years, with the interest compounded every 8 months at a rate of 15% per annum.

- Compounding period is 8 months, so there are 3 compounding periods (2 years = 24 months).

- Effective rate for 8-month compounding period: \((1+ \frac{15}{100})^{\frac{8}{12}} \approx 1.1\)

- Calculation: \(Rsx \times (1.1)^3 = Rs12,777.60\)

- Solving \(((1.1)^3 \approx 1.331)\): \(Rsx \approx \frac{12,777.60}{1.331}\)

- Rsx approximates to Rs9,600.

- Option:3 - Rs9600 is the correct answer.