Realize using NOR gates only?
Wont be appropriate to post full solution, but will point out your errors.


Your Kmap is unfortunately flawed. 
$$f(A,B,C,D) = \prod (0, 1, 2, 7, 8, 9, 10) + \Phi(12, 13)$$


Here, maxterms \$(12, 13)\$ are dont cares and you have to fill all other maxterms with 0s in Kmap and round the biggest groups of zeroes. But you have filled them with 1s as like minterms.


After rounding process, you will get an SOP expression for \$f'(A,B,C,D)\$. You have to take its complement to get the POS expression for \$f(A,B,C,D)\$ .