First, we will calculate Leslie's knitting rate per night. Leslie knit a total of 432 centimeters over 9 nights. To find the unit rate (centimeters per night), we divide the total centimeters by the total nights:
\[ \text{Rate} = \frac{432 \text{ centimeters}}{9 \text{ nights}} = 48 \text{ centimeters per night} \]
Now, we need to determine how many centimeters Leslie will have knit after 15 nights. We can do this by multiplying the rate by the number of nights:
\[ \text{Total centimeters after 15 nights} = 48 \text{ centimeters per night} \times 15 \text{ nights} \]
Calculating this gives:
\[ \text{Total centimeters after 15 nights} = 48 \times 15 = 720 \text{ centimeters} \]
Therefore, after 15 nights of knitting, Leslie will have knit a total of:
\[ \boxed{720} \text{ centimeters} \]
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