Let Nishu take x days to complete the work alone. 

∴ Total work done by Nishu in 1 day = \(\frac{1}{x}\) Also, Pintu takes (x + 6) days to complete the work alone.

∴ Total work done by Pintu in 1 day =\(\frac{1}{x+6}\)

∴ Total work done by both in 1 day = (\(\frac{1}{x}\) +  \(\frac{1}{x+6}\))

But, both take 4 days to complete the work together. 

∴ Total work done by both in 1 day = 1/4

According to the given condition ,

1/x + 1/(x+6) = 1/4

∴ x + (6+x) / x(x+6) = 1/4

∴ 2x + 6 / x(x+6) = 1/4

∴ 4(2x + 6) = x(x + 6) 

∴ 8x + 24 = x + 6x 

∴ x² + 6x – 8x – 24 = 0 

∴ x² – 2x – 24 = 0 

∴ x² – 6x + 4x – 24 = 0 

∴ x(x – 6)+ 4(x – 6) = 0 

∴ (x – 6) (x + 4) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get 

∴ x – 6 = 0 or x + 4 = 0 

∴ x = 6 or x = -4 

But, number of days cannot be negative, 

∴ x = 6 and x + 6 = 6 + 6 = 12

∴ Number of days taken by Nishu and Pintu to complete the work alone is 6 days and 12 days respectively.