In Kingdom Hearts Birth by Sleep, synthesis does not occur, instead there is Command Charge. In Command Charge, you mix 2 commands to form a new command. In Command Charge, like Item Synthesis, you can add materials, namely crystals, to add effects. By adding certain crystal such as Rolling crystal with a certain command, the resulting command will a support ability such halving its cool-down time or increasing damage.
Examples
For example, if you mixed Fire Blitz and Aero, you would get Aerial Slam. So if you added a Moisture Crystal to Fire Blitz and Aero, you would get an HP UP instead.