A family of Microsoft relational database management systems designed for ease of use.
Because you are trying to reference a sub form when you open your other form, the system does not recognize "[Forms]![Sample_Table_Subform]![Serial Number]." To reference a field or control on a sub form, you need to use the syntax: Forms![Parent Form Name]![Sub Form Control Name].Form![Serial Number].
However, because your button is located in the sub form, you need only do the following using VBA instead of a Macro:
Private Sub YourCommandButtonName_Click()
If (Not IsNull(Me.[Serial Number])) Then
DoCmd.OpenForm "Sample_Form", , , "[Serial Number]='" & Me.[Serial Number] & "'"
End If
End Sub