PEG-6, PEG-8, PEG-12, PEG-40, PEG-150, etc.
Polyethylene glycol is a family of long chain polymers made up of ethylene glycol subunits. The number after the name indicates the approximate molecular weight of the chain (higher numbers mean longer chains).
PEG is used as a thickener in many products. It is used in toothpaste to prevent bacteria from breaking down the pyrophosphates used to control tartar buildup.
PEGs are often reacted with fatty acids to make detergents that have thickening and foam stabilizing properties. When chemically combined with fatty acids from coconut oil, it makes detergents like PEG-5 cocamide, which is used in shampoos as a surfactant, emulsifier, and foam stabilizer.