what is the importance of step four as man in relation to the next step to be taken and the lady for the reverse turn

Is it that the man steps backward and the lady forward?

Yes can you tell me why is that step is important for the man to do correctly in this figure.

The man is stepping backwards on 4, but the character of the movement requires that he retains control. The THT footwork (with the heel only 'just' coming into contact with the floor) before rising back to the toe to step to another toe on 5 allows this control, and slows the man's flight down, to make it easier for the lady to now turn around him. In particular, having made a proper inside turn action between 4 & 5 (with a pointing alignment of LF), the man waits for the lady to come around, before slipping the RF OP in CBMP, leaving the body underturned, before stepping again (typically into a Three Step) with CBM.

Carol. Please write your answer then I may be able to sleep.

LOL.........

Carolmatthew. Several things are going on. On the Fourth and and most importantly the Sixth Step of the Reverse Turn. For the man the fourth step is THT. The sixth step which is in CBMP is a TH. This is a foot position only . Also the lady having the greater distance to travel must be allowed time to get into position that is why the mans body is facing the wall on step five. When the text books were first composed the words were chosen very carefully. CBMP is Contrary Body Movement Position. Notice the word Position ( where someone or something has been placed ) That is exactly what it means. Place that sixth step into Position.
I'm only guessing. But I think you might be being pulled of balance because of the the man's bad Technique.

Also look at the clip on this site or others on youtube. Look at exactly where the mans RF goes on step four. You will notice it is not straight down the LOD. And do we see the foot turned in very slightly, more towards an outside edge.

I agree that the placement of step 6 as man is very important: it's hardly a step, at all, but only just more than a cross in front of LF, allowing the lady to come around.

I don't agree, however, with the suggested direction of step 4. Standard technique has steps 3 & 4 aligned backing LOD (ie straight). It is the correct usage of CBM on step 4 that will result in a slight turn in of the toe (normal for any backward step with CBM) - but the foot should travel straight back.

Telemark. I've heard this argument so many times before. I always pose the same question. If the man and the lady both take a step straight down the LOD they will both be trying to occupy exactly the same space at the same time. This is where the books need to be corrected. The same can be said about step four of a Natural Spin Turn. The man must get out of the ladies way. That's why that step goes more towards diag to wall allowing the lady the straight line. Work it out for yourself. You will see that if that 4th step for the man is taken straight down the LOD the lady will have no choice but to do circular movement to get around. She should be taking the straight route. Even way back I was always instructed that the person going forward has the right of way. In this case it is the lady.
Finally. Make your way to Learn The Dances. Choose Reverse Turn and Feather Finish in the International Foxtrot and learn where that fourth step is supposed to go. You will no doubt observe now it has been pointed out that that step four does not go straight down the LOD for the man.
The shoulders. Now that's a different story. But we are talking about the foot position.