what is the sum coefficient and balanced equation of :

Co(OH)3+Na2CO3
my answer is
3Co(OH)3+ 3Na2CO3---> 3CoCO3+ 3Na2OH

You have changed the oxidation state of Co from III to II and you DON'T show a corresponding change for anything else.

So cobalt(III) carbonate will be Co2(CO3)3

Some other points I should make. Co(OH)3 is not very soluble in water. With no phases shown I doubt there would be anyreaction between two solids. Even with aqueous Na2CO3, the possibility of a reaction depends upon the solubility product of Co(OH)3 vs Cu2(CO3)3; i.e., which is more insoluble.