How to search 2 criteria using this search function?

I haven't tested but you can try this. You didn't say if both were required so this assumes both are.
If you need to paste something offset of the second search then you need to add the .value = X2.Offset(#,#).Value's in with the ones you already have below.

Dim strSrch As String
Dim rSrch As Range
Dim Search As Integer
Dim X As Range
Dim X2 As Range

'Search Criteria 1
Set X = Sheets("Sheet1").Range("B:B").Find(what:=Userform1.txt_sc.Value, LookIn:=xlValues, _
                    lookat:=xlWhole, SearchOrder:=xlByRows, SearchDirection:=xlNext, _
                    MatchCase:=False, SearchFormat:=False)

'Search Criteria 2
Set X2 = Sheets("Sheet1").Range("B:B").Find(what:=Userform1.txt_linenum.Value, LookIn:=xlValues, _
                    lookat:=xlWhole, SearchOrder:=xlByRows, SearchDirection:=xlNext, _
                    MatchCase:=False, SearchFormat:=False)

If X > 0 And X2 > 0 Then

    With Me
      .cb_region.Value = X.Offset(0, 4).Value
      .txt_requestor.Value = X.Offset(0, -1).Value
      .cb_clean.Value = X.Offset(0, 5).Value
      .txt_received.Value = X.Offset(0, 1).Value
      .txt_complete.Value = X.Offset(0, 2).Value
      .txt_pm.Value = X.Offset(0, 16).Value
      .txt_rmgr.Value = X.Offset(0, 17).Value
      .txt_wbse.Value = X.Offset(0, 6).Value
      .txt_so.Value = X.Offset(0, 8).Value
      .txt_partnername.Value = X.Offset(0, 9).Value
      .txt_partnernumber.Value = X.Offset(0, 10).Value
      .txt_linenum.Value = X.Offset(0, 7).Value
      .txt_lineamount.Value = X.Offset(0, 14).Value
      .txt_currency.Value = X.Offset(0, 20).Value
      .cb_type.Value = X.Offset(0, 21).Value
      .txt_rname.Value = X.Offset(0, 15).Value
      .cb_status.Value = X.Offset(0, 18).Value
      .txt_po.Value = X.Offset(0, 13).Value
      .txt_podate.Value = X.Offset(0, 12).Value
      .txt_remarks.Value = X.Offset(0, 19).Value
   End With

Else
           
End If