What is a 1964 Washington Quarter that is in a mint state of BU?

Even in mint state, (with the exception of very high grades like MS-67+ as graded by a reputable grading company) the coin isn't worth much more than the silver content, which at the time of writing is about $5.58. You might be able to get some more money if you shop around or sell it to collectors, but the more recent silver coins were produced in massive amounts with the 1964 year easily having the highest mintage of all silver quarters produced, and as such, it isn't a very desirable coin except for silver content.