Answer:
The answer is indeed "The best solution to the problem is to require parking permits."
Step-by-step explanation:
Formal language is most commonly used when writing. It takes vocabulary and grammar into full consideration, following grammar rules and avoiding some lapses that are usual in spoken language. Formal language also tries to be more impersonal. In the sentence "The best solution to the problem is to require parking permits", the person who should or will find the solution is not mentioned. The speaker also avoids saying "in my opinion" or "to my mind", which helps to keep the impersonality of the tone.
The other sentences that were offered as options are characterized with informal qualities: the use of "ain't" and "gonna", the use of a reflexive pronoun - themselves - where it is not necessary and so on. Those are traits of spoken, and very informal, language.