Solution in C#, first thing I did was realize that there is very little sorting necessary in this problem. What we have to do is find the sums of the x rows and the sums of the y columns. Once we've done that we sort both arrays and compare the arrays to ensure they match 1-to-1. If they do not, they are impossible to sort otherwise they are possible. I left my debugging code for brevity.

Essentially this swap sort method only works if each bucket has enough storage in it to hold the maximum count of a given item. (i.e. if there are two items of type A, there must be a corresponding bucket with two slots) this must be true for each item.

 public static string organizingContainers(List<List<int>> container)
{
    List<int> xSum = new List<int>();
    List<int> ySum = new List<int>();
    int localXSum = 0;
    int localYSum = 0;

    for(int i = 0; i < container.Count; i++){
        localXSum = 0;
        localYSum = 0;           
        for(int j = 0; j < container[i].Count; j++){
            localXSum +=  container[i][j];
            localYSum += container [j][i];
        }
        xSum.Add(localXSum);
        ySum.Add(localYSum);
    }

    xSum.Sort();
    ySum.Sort();

    foreach(int pos in xSum){
        Console.Write(pos + " ");
    }

    Console.WriteLine();

    foreach(int pos in ySum){
        Console.Write(pos + " ");
    }

    Console.WriteLine();

    for(int i = 0; i < xSum.Count; i++){
        if(xSum[i] != ySum[i]){
            return "Impossible";
        }
    }

    return "Possible";
}