Get date if category and month match

I have a workbook with Checking account register on sheet1, Budget on sheet2. Checking columns are Date, To/From, Category, Credit, Debit, Balance. Budget columns are Due Date, Category, Amt Due, Paid. I am trying to pull the date from checking on sheet1 and insert it in the budget column paid on sheet2, provided the category and month match on sheet1 and sheet2. Hope that made sense. Attached is the excel file. Really appreciate any and all help.