Need to sort by matching columns

I have a two spreadsheets with a lot of data on them that I am trying to make sure have been transcribed correctly from one to the other through manual entry. I suspect this is not the case and I want to identify the errors and fix them. I took the relevant columns from each sheet and put them next to each other on a new one. Column A shows part number and Column B the corresponding quantity. Column C shows part number from the second sheet, and again Column D has the corresponding quantity. Unfortunately, there is a vast discrepancy in number of lines, as Column A has many more part numbers in it than Column C does.

What I am attempting to accomplish is to have Excel find any exact matches between Columns A and C, and sort by that, while keeping the correct quantity data from Column B on the same row with its corresponding part number in Column A, and likewise for Columns D & C. Ideally, any rows that did not have a match, or where Column C was blank would be sorted to the bottom of the sheet.

Attached is a small piece of the sheet I am dealing with for simplicity's sake. The full file has more than 10,000 rows. Any help would be greatly appreciated. Thank you.

Try this code

Sub Macro7()

LCA = Range("A65536").End(xlUp).Row
LCC = Range("C65536").End(xlUp).Row

    Range("E1").FormulaR1C1 = "Matched QTY"
    
    Range("A2:D" & LCA).Select
    ActiveWorkbook.Worksheets("Sheet1").Sort.SortFields.Clear
    ActiveWorkbook.Worksheets("Sheet1").Sort.SortFields.Add Key:=Range("A2:A" & LCA) _
        , SortOn:=xlSortOnValues, Order:=xlAscending, DataOption:=xlSortNormal
    With ActiveWorkbook.Worksheets("Sheet1").Sort
        .SetRange Range("A1:D" & LCA)
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    
    Range("E2:E" & LCC).FormulaR1C1 = "=IF(ISNA(MATCH(RC[-2],R2C1:R" & LCA - 1 & "C1,0)),""Not Found"",OFFSET(R1C[-4],MATCH(RC[-2],R2C1:R" & LCA - 1 & "C1,0),1))"
    Range("F2:F" & LCC).FormulaR1C1 = "=IF(RC[-1]=RC[-2],""Ok"",""Error"")"
    
        Range("A1:F" & LCC).Select

    ActiveWorkbook.Worksheets("Sheet1").Sort.SortFields.Clear
    ActiveWorkbook.Worksheets("Sheet1").Sort.SortFields.Add Key:=Range("F2:F" & LCC) _
        , SortOn:=xlSortOnValues, Order:=xlDescending, DataOption:=xlSortNormal
    ActiveWorkbook.Worksheets("Sheet1").Sort.SortFields.Add Key:=Range("A2:A" & LCC) _
        , SortOn:=xlSortOnValues, Order:=xlAscending, DataOption:=xlSortNormal
    With ActiveWorkbook.Worksheets("Sheet1").Sort
        .SetRange Range("A1:F" & LCC)
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    
    Range("A!").Select
End Sub

Here's my interpretation of your problem.