It is not completely clear to me what you want to achieve but this solution works for these test values and the second column:

In your code I missed moving the selection in the sheet which I included here but it would be better to refer to cells in the sheet by the range rather than selecting cells anyway.
In the code I also included a method to print out the array after each step so you can check.
    Option Explicit
    Sub test()
    Dim arr As Variant, _
        mycell As Range, _
        i, j, k As Long
        arr = Range("F1:I8").Value
        Debug.Print "Starting Point"
        PrintArray arr
        Do
            For i = 2 To 2 'Just column 2 for now! normal: LBound(arr, 2) To UBound(arr, 2)
                Range("A1").Select
                For j = LBound(arr, 1) To UBound(arr, 1) 'Rows in that column
                    If arr(j, i) <> ActiveCell.Value Then
                        'shift down current column in array
                        For k = UBound(arr, 1) To j + 1 Step -1
                            arr(k, i) = arr(k - 1, i)
                            PrintArray arr
                        Next k
                        arr(j, i) = ActiveCell.Value
                        PrintArray arr
                    End If
                    ActiveCell.Offset(1, 0).Select
                    If ActiveCell = "" Then Exit For
                Next j
            Next i
        Loop While ActiveCell <> ""
    End Sub
    Sub PrintArray(a As Variant)
    Dim i, j As Long, _
        line As String
        For i = LBound(a, 1) To UBound(a, 1)
            line = ""
            For j = LBound(a, 2) To UBound(a, 2)
                If a(i, j) = "" Then
                    line = line + "--- "
                Else
                    line = line + Format(a(i, j), "000") + " "
                End If
            Next j
            Debug.Print line
        Next i
        Debug.Print
    End Sub
Output:
Starting Point
002 003 004 --- 
004 006 008 --- 
006 009 012 --- 
008 012 016 --- 
010 015 020 --- 
012 018 024 --- 
--- --- --- --- 
--- --- --- --- 
002 003 004 --- 
004 006 008 --- 
006 009 012 --- 
008 012 016 --- 
010 015 020 --- 
012 018 024 --- 
--- --- --- --- 
--- --- --- --- 
002 003 004 --- 
004 006 008 --- 
006 009 012 --- 
008 012 016 --- 
010 015 020 --- 
012 018 024 --- 
--- 018 --- --- 
--- --- --- --- 
002 003 004 --- 
004 006 008 --- 
006 009 012 --- 
008 012 016 --- 
010 015 020 --- 
012 015 024 --- 
--- 018 --- --- 
--- --- --- --- 
002 003 004 --- 
004 006 008 --- 
006 009 012 --- 
008 012 016 --- 
010 012 020 --- 
012 015 024 --- 
--- 018 --- --- 
--- --- --- --- 
002 003 004 --- 
004 006 008 --- 
006 009 012 --- 
008 009 016 --- 
010 012 020 --- 
012 015 024 --- 
--- 018 --- --- 
--- --- --- --- 
002 003 004 --- 
004 006 008 --- 
006 777 012 --- 
008 009 016 --- 
010 012 020 --- 
012 015 024 --- 
--- 018 --- --- 
--- --- --- ---