Count the number of occurrences of each fill color over an arbitrary range of cell?

Something like that could work. Loop through each Cell in the Rng and check its color.

Function lbrHrsTot(Rng As Range) As String
    Dim R As Long
    Dim G As Long
    Dim B As Long
    Dim Re As Long
    Dim Y As Long
    Dim S As Long

    Dim Cell As Range
    For Each Cell In Rng
        If Cell.Interior.Color = RGB(255, 0, 0) Then
            R = R + 1
        ElseIf Cell.Interior.Color = RGB(0, 176, 80) Then
            G = G + 1
        ElseIf Cell.Interior.Color = RGB(0, 176, 240) Then
            B = B + 1
        ElseIf Cell.Interior.Color = RGB(166, 166, 166) Then
            S = S + 1
        ElseIf Cell.Interior.Color = RGB(255, 192, 0) Then
            Y = Y + 1
        ElseIf Cell.Interior.Color = RGB(192, 0, 0) Then
            Re = Re + 1
        End If
    Next Cell

    lbrHrsTot = "Red " & R & " Green " & G & " Blue " & B & " Silver " & S & " Yellow " & Y & " Dark Red " & R
End Function

Consider using Select Case instead of the multiple If … ElseIf … End If.