As most folks have already pointed out, you need to change the way you are referencing the desired destination cell. Either you can switch over to an ampersand (&), or change to just a Cells(row,col) reference as you are only updating a single cell (see code below). You should also consider slimming down your code to make it a bit more efficient.
Dim destbook As Workbook
Dim destsheet As Worksheet
Set destbook = Workbooks("Book1")
Set destsheet = destbook.Sheets(1)
'See my note below
destbook.Activate
destsheet.Range("C6").Select
ct = Range(Selection, Selection.End(xlDown)).Count + 1
destsheet.Cells(ct, 1).PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks:=False, Transpose:=False
Notes:
- Line 5 should be changed to use your variables destbook and destsheet. Note that you'll need to move line 7 up to initially Activate your Workbook and then you can reference your Worksheet destsheet.
- At the "see my note below", you should probably be copying some value from somewhere, otherwise you'll run into a new error upon your PasteSpecial command.
- You should combine line 8 and line 9 together, unless you are planning on reusing the selection from line 8 in some other code (that you have not provided here).
Hope this helps.