(a) When compounded half-yearly:

Here, $P=800, R=20$ and $t=1$

$\therefore \quad CI =P\left[\left(1+\frac{R}{100 \times 2}\right)^{2 \times t}-1\right]$

$=800\left[\left(1+\frac{20}{100 \times 2}\right)^{2 \times 1}-1\right]$

$=800\left[\left(\frac{11}{10}\right)^{2}-1\right]=\frac{800 \times 21}{10 \times 10}=₹ 168$

When compounded quarterly:

$\begin{aligned} \text { Here, } P &=8000, R=20 \text { and } t=1 \\ \therefore \quad C I &=P\left[\left(1+\frac{R}{100 \times 4}\right)^{4 \times t}-1\right] \\ &=800\left[\left(1+\frac{20}{100 \times 4}\right)^{4 \times 1}-1\right] \\ &=800\left[\left(\frac{21}{20}\right)^{4}-1\right]=\frac{800 \times 34481}{20 \times 20 \times 20 \times 20} \\ &=₹ 172.40 \end{aligned}$

$\therefore \quad$ Difference $=₹(172.40-168)=₹ 4.40$