Answer
Coordination number: $6$
Oxidation number: $+3$
Work Step by Step
The ligands ( $(NH_{3})_{4}$ and $Cl_{2}$) that surround the central metal atom $Co$ are (4+2) $6$. Thus, the coordination number is 6.
Let us suppose the oxidation number of $Co$ is X. To find the oxidation number, we sum the known oxidation numbers and equal it to the charge on the complex.
$NH_{3} = 4 \times (0)$
$Cl_{2} = 2 \times (-1)$
The overall charge is zero on the complex, thus:
$X + 4 \times (0) + 2 \times (-1) -1 = 0 $
$X -2 -1 = 0$
$X -3 =0$
$X= +3$
Oxidation number of of $Co = +3 $
