Frankie back when he was 2 months old​

the choice that is not a technique that you should use to come up with ideas for the topic of a research project is, writing about academic subjects that are not interesting to you. this does not belong to the techniques to come up with ideas because having no interest in a certain topic will lose your drive to come up with better ideas. it gives no room for improvement and acquiring of new ideas and information. 

explanation:

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).