Rewriting this logic expression to NAND only ports
There are more ways of simplifying things than just de Morgan's rule.

Just like in multiplication/addition, there are also associativity and commutatively rules, for example:

$$A + B + C = (A+B) + C$$
$$A\cdot C + B\cdot C = C\cdot(A+B)$$

If you use those relationships in your simplification you do indeed end up with only 6 gates. It may be possible to get fewer still with care (seems 5 is possible from the comments).


   Hint: What do the first two terms of the original expression have in common?