It is worth noting that 1966 was the last year these quarters were made of the classic 90% silver composition before it was changed to a composition of 40% silver and 60% copper, known as a clad composition. As a result, older quarters (prior to 1965) can sometimes sell for much higher premiums, particularly if they remain in good condition.
Ultimately, the best way to determine the value of a 1966 Liberty quarter dollar coin is to have it appraised by a professional numismatist.