Activity reduces from $6000 \mathrm{dps}$ to $3000 \mathrm{dps}$ in 140 days. It implies that half-life of the radioactive sample is 140 days. In 280 days (or two half-lives)activity will remain $\frac{1}{4}$ th of the initial activity . Hence the initial activity of the sample is

$4\times 6000 \mathrm{dps}=24000 \mathrm{dps}$