Edsson :
Noob question. Can I have them both or they conflict with each other?
Direct3D is a component of the DirectX API suite which is designed to provide standardized access to the system's graphics hardware in a high-level fashion. Direct3D is architecture agnostic, it is the responsibility of the hardware manufacturer to create hardware and drivers that are compatible with the latest Direct3D API revision.
Mantle is a competitor to DirectX that is fine tuned for AMD's GCN architecture. Mantle is conceptually similar to Direct3D in many aspects, but provides a lower-level degree of control which in theory allows it to reduce software overhead and improve rendering efficiency.
Direct3D is installed alongside Windows, and the driver components are installed with the manufacturer's driver bundle.
Mantle is installed with AMD's driver bundle.
Both can be installed at the same time without issue, it is up to the game designer to decide which one to use.