The given F is in SOP form and it can be implemented using 5 NAND gates.
1 NAND to implement each term and 1 NAND for ORing the terms.
Now, we simplify the expression to get the POS form so that it can be implemeted using NOR directly.
F
=PQ+ QR+ RS+ST
=Q(P+R) + S(R+T)
=[ Q(P+R) + S ] . [ Q(P+R) + (R+T) ]
= [ (S+Q) . (S+P+R) ] . [ (R+T+Q) . (R+T+P) ]
This is in POS form and can be implemented using 5NOR gates directly - 1 NOR for each term and 1 NOR for ANDing the expressions.