Answer: Nishu takes 6 days and Pintu takes 12 days.
Let Nishu take \(x\) days; Pintu takes \(x + 6\) days. Work done in one day together \(= \frac{1}{4}\).
\[\frac{1}{x} + \frac{1}{x + 6} = \frac{1}{4}\]\[4(2x + 6) = x(x + 6)\]\[x^2 - 2x - 24 = 0\]\[(x - 6)(x + 4) = 0\]\(x = 6\). Check: \(\frac{1}{6} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4}\).