何以 is a classical/literary expression for 'why' or 'by what means'. In modern speech, 为什么 or 凭什么 are more common. 何以 lends a formal, literary, or rhetorical tone to speech and writing.
culture
The line 何以解忧，唯有杜康 is from Cao Cao's poem 短歌行 (Duan Ge Xing), written c. 208 CE. 杜康 is a legendary figure associated with the invention of wine and is used as a poetic synonym for alcohol.
