No problem and no need to try to unscrew the old rusted iron pipe.
Just cut the old 2" drain pipe off a few inches above the connection to the 6" with a pipe cutter or reciprocating saw with a metal cutting blade, and use a Fernco coupling or a no-hub coupling to connect either ABS black plastic or PVC white plastic pipe all the way back to the sink. Don't forget the 1/4" of slope per linear foot from the sink toward the main where it turns "horizontal".
A Fernco is a neoprene rubber sleeve with two stainless steel clamps around it to seal onto the plastic and the old pipe. A no-hub has a stainless steel sleeve over neoprene and is stronger and more rigid. Available at almost all plumbing supplies (big boxes, hardware stores, etc.). Fernco and no-hub connections meet most local codes for drain pipe.