A tetrahemihexahedron is like a funny looking shape that you can make if you take a cube (which is a shape with six square faces) and cut off four of the corners in a special way. It's like if you took a square block of cheese and cut off four tiny slices from each corner, but in a special way so that you were left with a weird four-sided shape instead of a cube.
This new shape has four triangular faces on top and four more on the bottom, and each of those triangles is the same size and shape. The sides of the shape are made up of six flat surfaces, sort of like the sides of a dice.
Imagine that the bottom of the shape is like a flat ground, and the top is like a roof that slopes down to the sides. But instead of being a regular sloped roof with a pointy tip, it's like somebody stretched the roof down so that it touches the ground in a straight line.
So, basically, a tetrahemihexahedron is a strange shape that's made by cutting off corners of a cube in a special way, and it has lots of triangular faces and six flat sides.