何其 is a literary/formal adverb used in exclamatory sentences to intensify an adjective, meaning 'how (so)!' or 'what (a)!' — similar to 多么 but more formal and often carrying a tone of surprise, admiration, or irony. It can also appear in rhetorical questions meaning 'how could it be that...?'. You'll mainly encounter it in written Chinese, classical-style prose, or formal speeches.