If I lived 8 months at a residence and 4 months in another, which address do I use?

For your tax return?  Use the address where you want to receive mail from the IRS now.

@b-bbwgirl , not knowing in ref. to what , it is only a guess below --

(a) for purposes of form 1040 or the state filings , you use the latest address  -- that is where you would receive your refund ( if checks )  and/or any notifications from the IRS  and/or the State

(b)  for purposes of homestead credit  ( in states like MI ), you show  first the  newest address and then the earlier address  as a renter or as a home owner

(c) for school district purposes , you have look at the state  instructions , but generally  you have to report both , most recent first and then the older one .

Hope this helps