To find out how many bottles the machine can fill in 8 hours, we can first determine the rate at which it fills the bottles.
The machine fills 5,400 bottles in 3 hours. To calculate the rate per hour, we can divide the total number of bottles by the number of hours:
\[ \text{Rate} = \frac{5,400 \text{ bottles}}{3 \text{ hours}} = 1,800 \text{ bottles per hour} \]
Now, to find out how many bottles it can fill in 8 hours, we multiply the rate by the number of hours:
\[ \text{Bottles in 8 hours} = 1,800 \text{ bottles per hour} \times 8 \text{ hours} = 14,400 \text{ bottles} \]
So, the machine can fill 14,400 bottles in 8 hours.