I like to trap each sink individually. So I would get a tailpiece extension to start and two p-traps. From the wall I would extend that pipe. It's gonna be a male end so instead of cutting pipe I would use 1-1/2"female adaptor. (Just a simple fix, I would cut the tee out in the wall but this will work just fine) Then extend the pipe out and put a wye to aim at both traps. Should be able to pickup the first one directly with the wye then extend out of it for the second.

So you'll need one 1-1/2" female adaptor, about 2ft of 1-1/2"pipe, two 1-1/2" p-traps, a double sided flanged tailpiece extension should cover both, glue (and primer if you use PVC instead of abs) Teflon tape and dope. The tape will just be for the male adaptor in the wall. The dope will be for all the other joints. Make sure to remember your washer from the flanged tailpiece to the basket strainer on your sink.

There's more than one watly to skin a cat. This is just the way I'd probably do it given the pics. The trouble will be bracing the pipe coming out. You'll need to put a pice of wood in there with a j hook or something. Best of luck friend. Inbox me if you have any questions