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The pic pretty much explains everything -- I need to create a draggable six-column average

A lot of people had a similar problem where they were averaging cells within one column; I, however, have to average cells within a row

I spent a lot of time tinkering with AVERAGE and OFFSET, but can't get it to work:
=AVERAGE(OFFSET($D$3,,(COLUMN(D3)-1)*6))
I was thinking about creating something along the lines of
AVERAGE([cell adjacent to the fixed reference cell to the right, times 6)]:[cell adjacent to the fixed reference cell to the right, times 6, then plus 6])
Any input will be greatly appreciated

Thanks!