Creating a majority gate using only NOR gates
You can implement any logic circuit using only NANDs, it doesn't mean you will use a single NAND. Try writing down how to implement the following logic gates using NANDs


AND
OR
NOT


With those you can definitely implement the function you have, but simplifying it will require either manipulating the boolean expression bcd + acd + abd + abc to write it with NANDs or using Karnaugh maps (but it is a bit different than the one for AND/OR simplification).