Joining an 2' x6' section of privacy fence to an 8'x6' section alrea

Please post a picture of your dilemma. That way we could see what you have to work with and then would be able to offer some suggestions. Without seeing the pieces and how they are built it is really hard to second guess what might work for you.

Just my experience, we had a post break off at the concrete last year, there's no way I'm digging 4' to get it out, and possibly having to repair the neighbor's sidewalk. You're working with a narrower panel so take it or leave it, but I used metal brackets and plates to fix ours. The L shaped ones on the support rails (2×4's in my case) to connect and I used the flat 6 hole plates to support the weight along the "good" posts at the ends (3 per end) to bear the weight of the panel better. I didn't pretty it up at all, but you could paint them to match if you're not into "industrial" 😉

you will a post on each side of the small fence section unless you plan on using it as a gate.

Oh my this is a tricky one and what I suggest is

I think Shauna's idea sounds pretty good to me, and fairly simple to do using the metal brackets.

Sorry my post got cut. What I'd suggest is attaching a board on the back to "bandaide" the 2 pieces together. It essentially just makes a wider board.