Hello there
Correct answer is letter C: His tips on finding buried treasure were believable: He had, after all, found buried treasure himself.
Letter A it's not possible because of the use of colons. Those are used like introductory devices, in many cases to give explanations, and "were believable" it's just an attribute given to "his tips". Besides, we do not usually add colons before the to be verb.
Letter B is neither possible because those are two independent clauses that has independent meaning; they make sense by themselve. Therefore, a comma would not be the best option to add in between them. In addition, in English Language, sentences are shorts and that one would be too long with a comma.
Letter C is the best option because of the correct use of the colons: it is giving an explation and the colons work like introductory devices in that case. :)
Hope this helps