Walk up to the washer while it is running a spin and watch what it does. A machine that moves on spin is giving you information. Your job is to sort that information into three groups: the load, the floor, and the leveling. Each group has its own short check, and you can run all three yourself.
Describe the walk exactly
Note what moves. Does the washer slide across the floor, rock on its feet, or bang the cabinet only at the top of the spin? Does it happen with a full load, a small one, or both? Note the point in the cycle where it starts. This description is your first record, and it decides which check comes next.
Check the load first
Stop the cycle and look at the drum. A single heavy item such as a rug, a blanket, or a pair of work boots can throw the drum off balance. Spread the load evenly, then run a small mixed load and watch whether the walk comes back. If it stops, the load was the cause, and the washer is doing what it should.
Check the leveling
Set a level on top of the washer, front to back and side to side. Turn each foot until the machine sits firmly on all four corners, then tighten the lock nuts against the cabinet. Check that the floor under the washer is solid and not soft at one corner. A machine that rocks on one foot will walk on spin even with a balanced load.
Check the shipping bolts and the drum supports
Confirm that the transit bolts and spacers were removed when the washer was installed. If they stayed in place, the drum cannot move on its suspension, and the sound will repeat. Look at the drum supports and the shock absorbers for visible wear. Note what you find.
Log the walk and the age
Write down the day, the load type, the leveling check, and the result. A written log tells the next person what was already tried. Age is a planning input, not a verdict. The Clothes Washer: typical service life and when to plan page on this site gives the typical service life and shows how to turn the install year into a planning date.