Cant use K-table according to lecturer.

 

No.

What you are basically trying to claim is that (a·b)' = (a'·b'), and it doesn't.

Even if it did, you still wouldn't be finished because you would need to express each of the factors in NAND form.

 

Whenever there is a Sum of Products expression that must be implemented with NAND gates, the only operation that must be applied to the SOP is double negation and a single level application of DeMorgan. However, if the SOP expression must be minimized to a simpler SOP, then that must be accomplished prior to the double negation. If a K-map is disallowed for the minimization, then just perform a Boolean minimization. A K-map is not necessary but can provide insight for the Boolean minimization. If I were in your situation, I would perform the Boolean minimization with a K-map on the side - and claim a flash of insight came from imbibing mass quantities.