VBA Coding - Macro Moving Data With Multiple Variables?

I'm working on a complex spreadsheet and I'm working on a complex spreadsheet system for pulling and measuring data. My VB programming skills are about minimal/average, so you may see me on here asking various questions . In any case, what I'm trying to do is create isolation macros for "Kickback" data (erroneous). I'm trying to remove data with certain criteria and isolate it on a separate "kickback" sheet for one for taking a second look at. I've made the easy macro of creating a new spreadsheet:

Sub Create_Kicbacks_Sheet()
' Create_Kicbacks_Sheet Macro
' Creates "Kickbacks" sheet for invalid information.
Sheets.Add After:=Sheets(Sheets.Count)
Sheets("Sheet4").Select
Sheets("Sheet4").Name = "Kickbacks"
Sheets("Kickbacks").Select
End Sub

This coding works correctly. The problem area I'm finding is the sorting data. My goal is to look at Columns A and B for certain criteria and either leave it alone, move it to the "Kickbacks" sheet or delete (due to not being necessary in data calculations). Basically, here's a synopsis of what I'm looking for:

if Column A = Y and Column B = Mandatory -> Leave Alone
if Column A = Y and Column B = Best Efforts -> Move Row to Kickbacks
if Column A = Y and Column B = Empty Cell -> Move Row to Kickbacks
if Column A = Empty Cell and Column B = Mandatory -> Move Row to Kickbacks
if Column A = Empty Cell and Column B = Best Efforts -> Delete Row

Here's the code I have in excel (modified from one I found online)... Which only is doing some of what I want it to do:

Sub Moveto_Kickbacks()
Dim r As Range, LR As Long
With Sheets("Data")
LR = .Range("A" & Rows.Count).End(xlUp).Row
Set r = .Range("A2").Resize(LR - 1)
.Range("A1").AutoFilter field:=1, Criteria1:=""
.Range("B1").AutoFilter field:=2, Criteria1:="Mandatory"

[code]....