Three bucket water puzzle

Question

You have three buckets, two big buckets holding 8 litres of water each and one small empty bucket that can hold 3 litres of water. How will you split the 16 litres of water to four people evenly? Each person has a container but once water is distributed to someone it cannot be taken back.

In this puzzle, we need to allocate 4 litres to each person. So I considered the initial state as below

8 8 0 [0, 0, 0, 0]

The values in the bracket are the water given to those 4 people. I tried the below steps

5 8 3 [0, 0, 0, 0]
5 8 0 [3, 0, 0, 0]
5 5 3 [3, 0, 0, 0]
5 5 0 [3, 3, 0, 0]
2 8 0 [3, 3, 0, 0]
0 8 2 [3, 3, 0, 0]
0 7 3 [3, 3, 0, 0]
0 4 3 [3, 3, 3, 0]
0 1 3 [3, 3, 3, 3]
0 0 3 [4, 3, 3, 3]

But I couldnt take it further by giving those 1 litre for rest of the 3 persons since there is a constraint that water given to person cant be retrieved back.
Any help/hint towards final solution is greatly appreciated.

Answer 1

8 8 0 [0 0 0 0]
8 5 3 [0 0 0 0]
8 5 0 [3 0 0 0]
8 2 3 [3 0 0 0]
8 0 3 [3 2 0 0]
8 3 0 [3 2 0 0]
5 3 3 [3 2 0 0]
5 6 0 [3 2 0 0]
2 6 3 [3 2 0 0]
2 8 1 [3 2 0 0]
2 8 0 [3 2 1 0]
0 8 2 [3 2 1 0]
0 7 3 [3 2 1 0]
3 7 0 [3 2 1 0]
3 4 3 [3 2 1 0]
6 4 0 [3 2 1 0]
6 1 3 [3 2 1 0]
6 0 3 [3 2 1 1]
8 0 1 [3 2 1 1]
8 0 0 [4 2 1 1]
5 0 3 [4 2 1 1]
5 3 0 [4 2 1 1]
2 3 3 [4 2 1 1]
0 3 3 [4 4 1 1]
0 0 3 [4 4 4 1]
0 0 0 [4 4 4 4]