I am completely lost

Joel, it is a good idea to diagram and list the rules. The rules are: (1) Each flavoring must be used 1x and can only be used 1x in any recipe; (2) Appetizers can only include 3 flavorings at most; (3) F >< N; (4) S >< T; (5) G == N.

Now we are told that lemongrass and paprika are in the same recipe. It can be Appetizer, or Main. Let's try Appetizer. By rules 3 and 4, the Appetizer recipe must include at least 2 of (F, N) and (S,T). If it has to include L and P too, it's not going to work because it will violate rule 2.

Hence, L and P must be in the Main recipe. There you have your answer.

Here is how you should diagram a problem like this. Notice that in this case (Appetizer), it is not possible to have L and P as ingredients without violating rule 2 that an appetizer can only include 3 flavorings at most.