If the nominal yearly rate is $8\%$, and we are compounding every half year, then the half-yearly rate is $\frac{8}{2}\%$, that is, $0.04$. So if we have $A$ in the bank, ater a half-year we have $A+A(0.04)$, that is, $A(1.04)$. So our investment gets multiplied by $1.04$ every half-year.
In the first half-year, it grows to $10000(1.04)$. In the next half-year, that gets multiplied by $1.04$, so at the end of the year we have $10000(1.04)(1.04)$, or more simply $10000(1.04)^2$.
But $10000$ of this is principal which is being repaid. The interest paid on the certificate at the end of the year is therefore $10000(1.04)^2-10000$. The result should be $816$.