The part of the Earth that is solid but has the ability to flow is the mantle.

Here's why:

* Solid: The mantle is primarily composed of solid rock, mostly silicate minerals.

* Flow: While solid, the intense pressure and heat deep within the Earth cause the mantle to behave like a very viscous fluid over extremely long periods. This slow, creeping movement is called convection, and it's a major driving force behind plate tectonics.

Think of it like this: Imagine a very thick honey. It's a solid, but if you apply enough pressure and wait long enough, it will slowly flow. The mantle behaves similarly due to the immense heat and pressure within the Earth.