Objective: Match white corners with its matching edge piece on the upper layer.
Restrictions: No down layer moves, solved slots can’t be moved to upper layer.
Method: I have developed a system for this step. It will take a while to understand the method but once you do, this step it will become very easy. All you need to do is get a white corner and its matching edge piece to the upper layer. How? Well if there is not a white corner all ready on the upper layer. Simply move one to the top layer with a left or right move followed by a U move (to transfer the corner to the upper layer) then reverse the left or right move so you don't destroy the edge you placed in step 1. Now that you have a white corner on the upper layer. Look at that corner piece ignoring the white and note the other two colours on the corner. What ever those two colours are that is the colours of the edge piece that you need to be on the upper layer to match it. Look for that edge piece if it is not on the upper layer. Move it to the upper layer the same way you moved a corner to the upper layer (remember to return your slice so stage 1 is intact). So now you should have a white corner piece and its matching edge piece on the upper layer. There are three different cases. All three are solved in the same manner. So don't worry all you need to learn is the method.
The first case is when the colour facing up on the corner piece is the same as the colour facing up on the edge piece. To solve rotate the upper layer so that the edge piece is in the upper/front or the upper/back. Now use the M slice to bring/hide the piece on the down layer. Now rotate the upper layer so that the corner is on the same side as the edge piece you hid with the white facing left or right. Then unhide the edge piece to bring it to the upper layer with a M move. This should match your corner and edge.
The second case is when the colour facing up on the corner piece is the opposite as the colour facing up on the edge piece. To solve rotate the upper layer so that the edge piece is in the upper/front or the upper/back. Now use the M slice to bring/hide the piece on the down layer. Now rotate the upper layer so that the corner is on the opposite side of the edge piece you hid with the white on the corner piece facing left or right. Then unhide the edge piece to bring it to the upper layer with a M2 move. This should match your corner and edge
The third case is when the colour facing up on the corner piece is white the colour facing up on the edge piece doesn’t matter in this case. To solve rotate the upper layer so that the corner piece is above a unsolved slot. Now use a L or R move to place the white corner piece so that the white is on a side (not facing up) but still remains on the upper slice. Then rotate the upper layer out of the way so when you return the L or R slice the corner remains on upper layer. This will turn the third case into either case one or case two. Simply solve that case to get your match.
Stage 2b. Placing matched pairs into there correct slot.
Objective: 2a) Place four matched pairs into their slots to complete left (green) and right block (blue).
Restrictions: no down layer moves, solved slots can’t be moved to upper layer.
Method: There is a number of ways to place matched pairs into their correct slots. Im just going to go through the most basic and easiest one to explain. So what is a slot? Slots are the location where we are going to put out matched pairs. The locations are the front / left (for the orange green pair) front / right (for the orange blue pair) the back/right (for the red blue pair) and the left / back (for the red green pair). SO after we have our corner matched to its proper edge it will already be on the upper layer. All we have to do is look at the colour that is facing up then rotate the upper layer till our matched pair is on along that side. ((( Red along the back, Orange along the front, green along the left and blue along the right))). Then we look at the colour that is on the side of our matched pair (the side not facing up). This is the slice we have to use to move the slot to the upper layer. Then insert the pair into the slot and reverse the last move to solve the slot. Sounds complicated huh. Well its actually super easy and will become second nature. You’ll be inserting with out thinking about it in no time... but until then I have all 8 possible slot insertions diagrammed below with the alg to insert it. Once you do a few you’ll understand the concept and shouldn’t really have to memorize the short alg.
pairs with red facing up
pairs with orange facing up
pairs with blue facing up
pairs with green facing up
So now you know how to match your corner with its edge and how to place that matched edge into its proper slot. Now all you have to do is pair a corner with its edge then insert it into its proper slot. Then move on to the next pair. Till all four slots are solved. After you have all four slots solved you should have a 2 by 3 block on the left and right side of the cube. Congratulations you have just finished the hardest stage.