After solving K-map We get the Output -
F= (z+w)(x'+y') => z(x'+y') + w(x'+y')
now taking Complement both side-
F' = ( z(x'+y') + w(x'+y') )'
F' = ( z(x'+y') )' . (w(x'+y') )'
again taking complement -
F = [ ( z(x'+y') )' . (w(x'+y') )' ]' we can also replace X' + Y' = (XY)'
This can be implemented using 4 NAND gates i.e given circuit in the solution above.