A friend of mine recently asked me about a move he had just been taught. His instructor called it an "Advanced Box". Steps 1,2,3 are that of a left turn, but on 3, the feet are together and the couple are in Promenade facing BLOD. There is a weight change on all 3 steps. During steps 4,5,6 the man steps as he would in a left turning box, but on step 4 the lady has to swivel her left foot in between the man's feet and then steps 5 and 6 are like that of a left turning box. My question: is there another name for this step? Thank you.

According to the Smooth Syllabus guidelines outlined by NDCA, you can also call it a Fallaway Reverse Turn with a Slip Pivot.

It is most definatly a fallaway. Sounds like the fallaway and box from the american waltz bronze syllabus.

Fallaway reverse and slip pivot, International Ballroom Gold level

I don't think this is Fallaway Reverse and Slip Pivot because you say the feet are together on step 3; that's not the way we were taught the figure by at least two professional instructors. It sounds more like steps 1-6 of a Bronze Fred Astaire figure called "Fallaway and Rock" (I'm not sure if it's still in the FA syllabus).

As we were taught the figure, years ago:
Steps 1-3 Bronze Twinkle
Steps 4-6 Step 4 is a Slip Pivot (though the instructor may not mention it at that level), steps 5 & 6 essentially finish the box, though we were not taught to close the feet on 6. We learned to end this part ready for the next 3 steps.
Steps 7-9 Left turning rock turn (about 1/2 L) with the feet held in CBMP
Steps 10-12 Steps 4-6 of a left box turning 1/4 L

You can find the details of a Slip Pivot in a lot of reference works.