It is a cuboid
In its most general form, a parallelepiped.
A cuboid fits the description given
Every rectangular prism does. That includes cubes.
A cuboid can have 6 rectangular faces, 12 edges and 8 vertices
A 3-d shape with 6 equal faces is a cube. It has 6 squares as it's faces. A 3-d shape with 6 equal faces and only 2 squares is a rectangular prism. It has 2 squares and 4 other rectangles (squares are rectangles too) as it's faces.
There is no 3D shape with 6 faces: 4 rectangles and 2 triangles. See the link for all forms of hexahedra.