You have an array of integers, and for each index you want to find the product of every integer except the integer at that index.

productExceptSelf.java

// 1   2   3   4  nums
// 1   2   6   24 forward
// 24  24  12   4 backward
// 24  12   8   6 final nums    
public int[] productExceptSelf(int[] nums) {
    return getProductExceptSelf(nums, buildForward(nums), buildBackward(nums));
}

private static int[] buildForward(int[] nums) {
    int[] forward = new int[nums.length];
    forward[0] = nums[0];

    for(int i = 1; i < nums.length; i++)
        forward[i] = forward[i-1] * nums[i];

    return forward;
}

private static int[] buildBackward(int[] nums) {
    int[] backward  = new int[nums.length];
    backward[nums.length-1] = nums[nums.length-1];

    for(int i = nums.length-2; i >= 0; i--) 
        backward[i] = backward[i+1] * nums[i];

    return backward;
}

private static int[] getProductExceptSelf(int[] nums, int[] forward, int[] backward) {
    nums[0] = backward[1];
    nums[nums.length-1] = forward[nums.length-2];

    for(int i = 1; i < nums.length-1; i++)
        nums[i] = forward[i-1] * backward[i+1];

    return nums;
}