We know that she filled 1/3 of the container before using 4L to fill it the rest of the way. This means that 4L = 2/3 of the bucket. Therefore, we now know that the bucket can hold 6L. The problem states that she fills the bucket. Now we just need to convert the liters to milliliters.
[tex]6 * 1000 = 6000mL[/tex]
And there is your answer! I hope this helped! If so, please leave a thanks. Have a blessed day!