Rubik's Cube Solver Code: Taking Too Long

Hey guys, Connor here.
I made a program that solves a Rubik's cube if you enter all the colors.
It works okay, but it takes so long. It takes 30 seconds to solve a 6
turn solution and about 10 minutes to solve a 7 move solution. I've seen
it done before in 8 moves in only 20 seconds. I was trying to look over
my code so that I could find what was making it slow down. I commented
out the part of the code that actually checks every solution, and it still
took a long time. This must mean that the part that is taking a while is
the part that simulates every combination of 'n' moves. Here is the code
that solves the cube.

public void solveIt() {
		int[] turns = new int[12];
		int[] moves = new int[numOfTurns];
		for(int i=0;i<12;i++) {
			turns[i] = i;
		}
		for(int i=0;i<numOfTurns;i++) {
			moves[i] = -1;
		}
		for(int i=0;i<numOfTurns;i++) {
			displayMoves[i] = "-";
		}
		for(long w=0;w<Math.pow(12,numOfTurns);w++) {
			moves[0]++;
			for(int u=0;u<numOfTurns-1;u++) {
				if(moves[u]==12) {
					moves[u+1]++;
					moves[u]=0;
				}
			}
			bestCheck(moves);
			System.out.print(1.0*w/Math.pow(12,numOfTurns));
		}
		for(int z=0;z<numOfTurns;z++) {
			if(bestMoves[z]==0) {
				displayMoves[z] = "F";
			}
			else if(bestMoves[z]==1) {
				displayMoves[z] = "R";
			}
			else if(bestMoves[z]==2) {
				displayMoves[z] = "U'";
			}
			else if(bestMoves[z]==3) {
				displayMoves[z] = "L";
			}
			else if(bestMoves[z]==4) {
				displayMoves[z] = "D'";
			}
			else if(bestMoves[z]==5) {
				displayMoves[z] = "B";
			}
			else if(bestMoves[z]==6) {
				displayMoves[z] = "F'";
			}
			else if(bestMoves[z]==7) {
				displayMoves[z] = "R'";
			}
			else if(bestMoves[z]==8) {
				displayMoves[z] = "U";
			}
			else if(bestMoves[z]==9) {
				displayMoves[z] = "L'";
			}
			else if(bestMoves[z]==10) {
				displayMoves[z] = "D";
			}
			else if(bestMoves[z]==11) {
				displayMoves[z] = "B'";
			}
			else {
				displayMoves[z] = "-";
			}
		}
		System.out.print(displayMoves[0]);
		for(int q=1;q<numOfTurns;q++) {
			System.out.print(", " + displayMoves[q]);
		}
		System.out.println();
		System.out.println("Solutions: " + solutions);
		System.out.println("BestCorrect: " + bestCorrect);
		for(int i:bestMoves) {
			if(i==0) mFace[0].rotateCW();
			if(i==1) mFace[1].rotateCW();
			if(i==2) mFace[2].rotateCW();
			if(i==3) mFace[3].rotateCW();
			if(i==4) mFace[4].rotateCW();
			if(i==5) mFace[5].rotateCW();
			if(i==6) {
				mFace[0].rotateCW();
				mFace[0].rotateCW();
				mFace[0].rotateCW();
			}
			if(i==7) {
				mFace[1].rotateCW();
				mFace[1].rotateCW();
				mFace[1].rotateCW();
			}
			if(i==8) {
				mFace[2].rotateCW();
				mFace[2].rotateCW();
				mFace[2].rotateCW();
			}
			if(i==9) {
				mFace[3].rotateCW();
				mFace[3].rotateCW();
				mFace[3].rotateCW();
			}
			if(i==10) {
				mFace[4].rotateCW();
				mFace[4].rotateCW();
				mFace[4].rotateCW();
			}
			if(i==11) {
				mFace[5].rotateCW();
				mFace[5].rotateCW();
				mFace[5].rotateCW();
			}
		}
	}
	public boolean bestCheck(int[] array) {
		for(int i:array) {
			if(i==0) mFace[0].rotateCW();
			if(i==1) mFace[1].rotateCW();
			if(i==2) mFace[2].rotateCW();
			if(i==3) mFace[3].rotateCW();
			if(i==4) mFace[4].rotateCW();
			if(i==5) mFace[5].rotateCW();
			if(i==6) {
				mFace[0].rotateCW();
				mFace[0].rotateCW();
				mFace[0].rotateCW();
			}
			if(i==7) {
				mFace[1].rotateCW();
				mFace[1].rotateCW();
				mFace[1].rotateCW();
			}
			if(i==8) {
				mFace[2].rotateCW();
				mFace[2].rotateCW();
				mFace[2].rotateCW();
			}
			if(i==9) {
				mFace[3].rotateCW();
				mFace[3].rotateCW();
				mFace[3].rotateCW();
			}
			if(i==10) {
				mFace[4].rotateCW();
				mFace[4].rotateCW();
				mFace[4].rotateCW();
			}
			if(i==11) {
				mFace[5].rotateCW();
				mFace[5].rotateCW();
				mFace[5].rotateCW();
			}
		}
		int num = correctCounter();
		if(num>bestCorrect) {
			bestCorrect=num;
			for(int r=0;r<numOfTurns;r++) {
				bestMoves[r] = array[r];
			}
			
		}
		for(int q=numOfTurns-1;q>=0;q--) {
			int i = array[q];
			if(i==6) mFace[0].rotateCW();
			if(i==7) mFace[1].rotateCW();
			if(i==8) mFace[2].rotateCW();
			if(i==9) mFace[3].rotateCW();
			if(i==10) mFace[4].rotateCW();
			if(i==11) mFace[5].rotateCW();
			if(i==0) {
				mFace[0].rotateCW();
				mFace[0].rotateCW();
				mFace[0].rotateCW();
			}
			if(i==1) {
				mFace[1].rotateCW();
				mFace[1].rotateCW();
				mFace[1].rotateCW();
			}
			if(i==2) {
				mFace[2].rotateCW();
				mFace[2].rotateCW();
				mFace[2].rotateCW();
			}
			if(i==3) {
				mFace[3].rotateCW();
				mFace[3].rotateCW();
				mFace[3].rotateCW();
			}
			if(i==4) {
				mFace[4].rotateCW();
				mFace[4].rotateCW();
				mFace[4].rotateCW();
			}
			if(i==5) {
				mFace[5].rotateCW();
				mFace[5].rotateCW();
				mFace[5].rotateCW();
			}
		}
		if(bestCorrect==48) {
			return true;
		}
		else {
			return false;
		}
	}
	public int correctCounter() {
		int num = 0;
		solutions++;
		String pieceCheck = "";
		String centerCheck = "";
		for(int h=0;h<6;h++) {
			for(int j=0;j<8;j++) {
				pieceCheck = "" + mFace[h].getColor(j);
				centerCheck = "" + mFace[h].getCenterColor();
				if(pieceCheck.equals(centerCheck)) {
					num++;
				}
			}
		}
		return num;
	}

If anyone can see a spot in my code that may be taking a long time, I
would be glad to hear your ideas or solutions.
Thanks,
Connor