After 280days , the activity of a radioactive sample is 6000 dps ....

Activity reduces from $6000dps$ to $3000dps$ 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 $\dfrac{1}{4}$ th of the initial activity . Hence the initial activity of the sample is

$4 \times 6000dps = 24000dps$