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Let $T_1$ and $T_2$ be time period of earth and satellite respectively then we have $8=\large\frac{2 \pi}{w_1+w_2} = \frac {2 \pi}{\large\frac{2 \pi}{T_1}+\large\frac{2 \pi}{T_2}}$

When earth and satellite are rotating in opposite sense.

$T_1=24 \;hrs$

$8=\large\frac{1}{\Large\frac{1}{24}+\frac{1}{T_2}}$

$T_2=12 hours$

When the earth and satellite are rotating in same sense.

$t=\large\frac{2 \pi }{\Large\frac{2 \pi}{T_1 }- \frac{2 \pi }{T_2}}$

$t=\large\frac{1}{\Large\frac{1}{24}-\frac{1}{12}}$

$t=24\; hours$

Hence d is the correct answer.

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