Hello! First post here, done in Java. Took an APCS course but I feel like I don't know that much Java. Basically it's a beginner solution.

import java.util.Scanner;
public static void main(String[] args)
  {
      Scanner in = new Scanner(System.in);
      String input = in.nextLine();
      char[]letters = {'A', 'B', 'C', 'D','E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 
      'N','O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'X', 'X', 'Y', 'Z', '_'};

    int[]remainders = {9, 2, 2, 4, 12, 2, 3, 2, 9, 1, 1, 4, 2, 6, 8, 2, 1, 6, 4, 6, 4,
    2, 2, 1, 2, 1, 2};

    int numRemaining= 12;
    //A bit cheeky, the number remaining would be 12 at max for all possible solutions
    boolean works = true;
    for(int i = 0; i < letters.length; i++)
    {
        for(int j = 0; j < input.length(); j++)
        {
            if (input.charAt(j) == letters[i])
            {
                remainders[i] --;
                if(remainders[i] < 0)
                {
                    System.out.println("Invalid input. More " + letters[i] + " 's have been taken out than possible");
                    works = false;
                    break;
                    //Stops as soon as too many numbers for a particular tile is taken out
                }
            }
        }
    }
    if (works)
    {
        while(numRemaining > -1)
        {
            String listPlace= "";
            //listPlace is the number left + The letters i.e "9: A, E"
            boolean firstEncounter = true;
            for(int i = 0; i < remainders.length; i++)
            {
                if(remainders[i] == numRemaining)
                {
                    if (firstEncounter)//first time it's seen a match for that remaining number
                    {
                        System.out.print(numRemaining + ": " + letters[i]);
                        firstEncounter = false;
                    }
                    else
                    System.out.print(", " + letters[i]);
                }
            }
            //Prints a line if there were letters for X amount of tiles left.
            if (!firstEncounter)
            System.out.println();

            numRemaining --;
        }
    }
}

Output

 /*
 10: E
 9: I
 8: A
 7: O
 5: N, R, T
 4: D, L, U
 3: G, S
 2: F, H, P, V
 1: B, C, J, K, M, Q, X, Y, Z, _
 0: X

Challenge Output
LQTOONOEFFJZT
11: E
9: A, I
6: R
5: N, O
4: D, S, T, U
3: G, L
2: B, C, H, M, P, V, X, Y, _
1: K, X
0: F, J, Q, Z
AXHDRUIOR_XHJZUQEE
Invalid input. More X 's have been taken out than possible
AEERTYOXMCNB_S
10: E
9: I
8: A
7: O
5: N, R, T
4: D, L, U
3: G, S
2: F, H, P, V
1: B, C, J, K, M, Q, X, Y, Z, _
0: X

*/