You will need to combine the two calculations : (parellelperiod and current member to make the set within the AVG function).
WITH MEMBER [Measures].[Last 6 Members Average] AS
AVG(
(
{
PARALLELPERIOD([Order Date].[Date].[Date], 5, [Order Date].[Date].currentmember) :
[Order Date].[Date].currentmember
},
[Measures].[Internet Order Quantity]
)
)
SELECT
{ [Measures].[Internet Order Quantity], [Measures].[Last 6 Members Average] } ON COLUMNS,
[Order Date].[Date].[Date].[ALL].children ON ROWS
FROM [Sales Cube]
Fitz