If the total work is \( W \), and Ravi finishes \( \frac{3}{4} \) of it in 12 days, the total time to complete the work is:
\[
\text{Total time} = \frac{12}{3/4} = 16 \, \text{days}
\]
To find the time for \( \frac{1}{2} \) of the work:
\[
\frac{1}{2} \times 16 = 8 \, \text{days}
\]
Thus, Ravi needs 8 days to complete \( \frac{1}{2} \) of the work.