__________ hard he tried, he could not succeed.

The correct answer is "However". This sentence uses a concessive conjunction to express a contrast or a situation where a particular effort or condition does not prevent a certain outcome. "However" is used in this context to mean "no matter how" or "to whatever extent." It introduces a subordinate clause that describes a condition that, despite its intensity, does not alter the result stated in the main clause. The typical grammatical structure for this usage is "However + adjective/adverb + subject + verb." In this specific sentence, "However hard he tried" effectively means "No matter how hard he tried," emphasizing the significant effort made without achieving success. The other options are grammatically incorrect or do not convey the intended meaning of concession. "Whatever" would imply "whatever thing," which does not fit with the adjective "hard." "Whenever" refers to time, and "Wherever" refers to place, neither of which makes sense in this context. Therefore, only "However" correctly expresses the idea of trying with great effort but ultimately failing, making it the appropriate choice for conveying this strong contrast.