"Towaway" Natural Recordings by Native Speakers
"Two way" means going both in two directions, often referring to communication, flow, or exchange between two parties. However, the term "tow away" is more common and it means to move or drive a vehicle, often a car, to a different location, typically because it is broken down or parked in a restricted area.
However, I believe you are referring to the word "towaway" as it is often associated with the traffic sign. A tow-away sign is a sign that indicates that vehicles parked in an area can be towed if not moved or if not in compliance with parking regulations.
A rope used to pull or tow something, typically a vehicle or trailer, especially in a horizontal or diagonal line.
A vehicle, typically a large truck, used to transport disabled or broken-down vehicles, industrial equipment, and other large loads. It is equipped with a winch and a flatbed for lifting and carrying heavy objects.