To find out how many nights Justine will need to spend knitting to complete a total of 96 centimeters of scarf, we first need to calculate the unit rate, which is the amount of scarf knitted per night.
Justine knitted a total of 48 centimeters over 8 nights. We can find the unit rate by dividing the total centimeters by the number of nights:
\[ \text{Unit rate} = \frac{48 \text{ cm}}{8 \text{ nights}} = 6 \text{ cm/night} \]
Now, we want to find out how many nights it will take to knit 96 centimeters. We can use the unit rate to calculate the number of nights:
\[ \text{Number of nights} = \frac{96 \text{ cm}}{6 \text{ cm/night}} = 16 \text{ nights} \]
Therefore, Justine will need to spend 16 nights knitting in order to knit a total of 96 centimeters of scarf.