Here's why:
* Pronoun Case: The rule you're referring to is about pronoun case. You need to use the objective case of a pronoun when it's the object of a verb or preposition.
* "I" is the nominative case (used for the subject of a verb).
* "Me" is the objective case (used for objects).
* Breakdown of the sentence:
* Paul is the subject (performing the action).
* gave is the verb.
* the flower is the direct object (what was given).
* to Ted and me is a prepositional phrase, with "to" as the preposition and "Ted and me" as the objects of the preposition.
Therefore, "me" is the correct pronoun to use in this case.