, "no, move with your hips." I haven't figured out yet how to walk using my hips first, but I think it has something to do with projecting your centre of gravity forward while coordinating the front foot at the same time so you don't get off balance.
Well, here's what I do. I'm sure others will jump in with both critiques of what I say - which is fine, I'm not saying this is all correct, just my best effort to articulate what it feels like I'm doing - and also with alternate explanations or methods. So take with grains of salt as one person's exploration.
Don't think of "hips" in this context as the big lateral joint on the far outside of your body where the top of the femur meets your pelvis, but as the whole belly/pelvis complex.
It should only take a couple of moments experimenting standing to figure this out.
Going to start without walking, just weight shifting. Stand in neutral posture, feet apart evenly weighted. Let your entire center (NOT just the little point two inches below belly button) slightly lift and settle down to the left. You'll feel corresponding movement in the left and right hips (groin, actually) as one opens and one closes and your weight shifts to your left foot without you moving a leg or foot. Repeat on the other side.
Now go into hamni and do is moving forward and back, again without stepping (basically, doing rowing exercise w/o the arms), having your entire center lift and shift forward, lift and shift back. You'll feel it in tummy and pelvis. Don't put any focus on feet or legs.
Once you can feel that...then try using this center-based weight shift to unweight your back leg so you can move it forward. Then smooth it out so your center can do less of the rise and just move forward, just a little ahead of your legs. Makes for fairly small steps that stay under your center.
ADDING TO THIS: actually for full integration, I DO engage the leg but I feel it as "pushing off" so much as maintaining a connection with the ground and running energy up from the ground TO the center.