Run a Query without Saving it (to reduce # objects)

Okay, so "Like" works, as would other approaches, when working with embedded digits in a larger number. 

Yes, I missed out on removing the left square bracket. 

To return to the SQL Syntax then ExcelBOA.[Account Number] is a number, not a string of  digits in a text field.

Private Sub cmButtonNameGoesHere_Click()

Dim strSQL As String

strSQL = "SELECT import_Excel_BOA.[As of Date], import_Excel_BOA.Amount," & _
        " import_Excel_BOA.[Account Number], " & _
        " import_Excel_BOA.[Account Name], import_Excel_BOA.Text " & _
        " FROM import_Excel_BOA " & _
        " WHERE (import_Excel_BOA.[Account Number] Like ""*"" & [Enter 5213 for VW1 or 5636 for VWMC] & ""*"")" & _
        " AND (import_Excel_BOA.Text Like ""*"" & [enter part of co name] & ""*"") ;"

Me.ListBoxNameGoesHere.RowSource = strSQL

End Sub

That's as close as I can get working without data to validate against. I think I got all of the open and close parentheses in the right places, the square brackets where they are needed, and the quotes and double quotes in the right places and numbers.