The steps are as follows:
The first time: B and A pass, and then B returns; Leave one on the other side
The second time: C and B pass, and then B returns; Leave a and c on the other side
Third time: A and B pass, and then A and A return; Leave one on the other side
The fourth time: A and C pass, and then C returns; Leave a, b and c on the other side.
The fifth time: A and B pass, and then A returns; Leave a, b, c and b on the other side.
Sixth time: A and C are both here.
At this point, all six people crossed the river safely.