Solid mahogany wood furniture is difficult to distinguish from a good mahogany veneer glued to the surface of a lesser quality wood. Veneer is a thin slice of wood, in this case mahogany, that is carefully attached to the surface to trick the eye into thinking the piece is solid wood. A short checklist will help you decide whether a piece is solid mahogany or simply mahogany veneer.
Look at the edges of the furniture to see if there is band of wood that has wood grain going in a different direction than the top area. Tabletop edges are locations where banding is easy to see. If you see banding, it is a veneer covering up the edge of the wood that was used to construct the piece of furniture. A table with banding is not a solid mahogany piece of furniture.
Check the back and underside of the furniture to see if it is the same wood as the surface. If the type of wood is different from that on the finished surface, the piece is not solid mahogany. A common practice is to put better quality wood on the surface and a lesser quality of wood underneath.
Look at the wood grain on the surface and follow it through to the edges. If the wood grain continues from the top over the edge and matches, the furniture is made from solid wood. If it does not match, the piece is at least partially made with veneer.
Look at the surface of the piece of furniture and notice whether all the wood grain is going in the same direction. When multiple directions of wood grain exist on the surface, the piece is made with veneer.