2x3x3 Cube

Note that U and D would be 90-degree turns on this cube, but each of L,R,F,B would be a 180-degree turn. Of course, this assumes you're holding it so that the two 3x3 parts are stacked on top of one another vertically.

Step 1

What I do first is get the edge cubies on one side resolved. Super easy.

Step 2

Now do the corners. An easy commutator is Li,U,R,Ui,L,U,Ri. Varients of this are easy to find.

Step 3

At this point, one 3x3 side is finished, and only the other 3x3 side remains. Use the well-known sequence X,Y,Xi,Yi with X=R,U,Ri,Ui and Y=Li,Ui,L,U to permute edge cubies. Then use the sequence in step 2 with a setup to get the corners in place. If they can't be tri-cycled into place, go to step 4; otherwise, you're done.

Step 4

If you get into a state where two edges need to swap, no tri-cycle will work. In this case, I execute the sequence R,Ui,Ri,U,R. This sets you back to step 2, but once done, the solve will go through.