Both of you may want to clarify the steps by being a little bit more dsecriptive. Int'l style has a clear and precise naming convention. But American style step names are quite ambiguous. One step may have three or four different names, depending on who you talk to. And one name may be used to describe three or four different steps, depending on who you talk to.
Case in point: The word "parallel" is known in the Arthur Murray schools to mean outside partner position, while in the Fred Astaire system it is used to describe shadow or side-by-side (tandem) position. So when Ms.Twinkle spoke of the Parallel Walks, we weren't sure whether she meant walks in shadow position or outside partner position.
Another ambiguous word is Twinkle. To some, a Twinkle is three steps, like a box step, where the third step turns to PP, to be followed by a closed finish or chasse in PP. To others it is three passing steps to PP. It can also be a series of forward or backward change steps taken O.P. (no promenade at all), or the same thing with feet passing. In an Alex Moore Popular Variations book, I've even seen the word Twinkle used to describe nothing other than a plain old box step.
Just something to keep in mind when discussing American style.
Anyway, if by "Parallel Walks", Ms.Twinkle was referring to a set of forward Changes taken Outside Partner, here's my suggestion: Do an even number of them, say, two or four, then follow with a forward check oustide partner: Man steps forward LF O.P. on count 1, lady back RF, then hold 2,3. Lady can optionally do a develope (kick L. leg) on 2,3 while man is holding. Then follow with the second half of a basic Box Step with 1/4 turn left (1st step lady forward O.P.). End facing diagonal center.
Sincerely,
Jonathan Atkinson