SQL Server 2012 Query: Invoices with Earliest Date in State for each Vendor
Looks like you don't have InvoiceState anywhere in your query.

Here it is with a little better formatting (PRE-COLUMN COMMA MASTERRACE!!)

SELECT VendorName
, InvoiceNumber
, InvoiceDate
, InvoiceTotal 
FROM Vendors V 
JOIN Invoices I 
    ON V.VendorID=I.VendorID 
WHERE InvoiceDate &lt;= ( SELECT Min(InvoiceDate) 
                       FROM Invoices 
                       JOIN Vendors 
                       ON V.VendorID=Vendors.VendorID ) 
GROUP BY VendorName
, InvoiceNumber
, InvoiceDate
, InvoiceTotal


Adding it (InvoiceState) to your SELECT and GROUP BY would add that level of detail.  I'd assume you need to add it as your first column (before VendorName).

Edit: looking at it further, seems like you'd also need it in your Subquery.