Answer
Tetraamminedichlororhodium(III) chloride.
Work Step by Step
1. In $[Rh(NH_{3})_{4}Cl_{2}]Cl$ $[Rh(NH_{3})_{4}Cl_{2}]$ is the cation whereas $Cl$ is the anion. Cations are named first then are anions.
2. In order to name the cation, Ligand is named first then is the metal. There are two ligands. These are alphabetically named, Tetramminedichloro.
3. Rh is Rhodium
4. In order to find the oxidation state of the metal, we add the charges and equal it to the charge on the complex, in this case zero. $NH_{3}$ is a molecule, it has 0 oxidation state. Thus,
$x-2-1 =0$
$x-3=0$
$x= +3$
Thus the oxidation state is +3 on the metal. Hence,
the name of the complex is tetraamminedichlororhodium(III) chloride
