东 + [verb 1] + 西 + [verb 2]
东 + [verb][verb] + 西 + [verb][verb]
东 + 一 + [measure word] + 西 + 一 + [measure word]
东…西… splits two related one-syllable verbs between 东 "east" and 西 "west". The directions stop meaning compass points: the frame says the action is scattered, going this way and that without order. Most uses are fixed four-character phrases.
The common ones:
Most of these describe disorder or restlessness – someone nervous, aimless or careless. 东奔西走 can also simply mean working hard and travelling a lot.
In speech the frame is open with a doubled verb: 东看看西看看, 东摸摸西摸摸. With 一 + measure word it says things lie scattered around, or that someone talks in no order.
The four-character phrases are complete in themselves and take no object. Add 地 and a second verb that takes it.