"Two dogs strive for a Bone, and a third runs away with it".
ur chinese is prtty good, i like it!
we put '你的最爱惜的汉语名言是什么?' as '你最喜欢的汉语（or 中国）名言是什么？'.
爱惜 means cherish, while 喜欢 means love, appreciate(value highly).
i suppose u r intending 谚语、格言（ an adage, proberb,or saying) by '名言（quotations）. my favorate is ' good good study and day day up'. :)