With each player in a game of Scrabble or Words With Friends getting 7 letters at a time on their rack, 6-letter words can play a huge part in deciding who will win and who will lose a game.
The 6-letter words containing Y on this list are worth 12.9 points on average.
But the best of the lot is worth a grand total of 36 in a game of Scrabble and that word is QUAZZY.
If none of the 2962 words on this list meet the criteria that you are looking for then you may find some success with similar lists: 6-letter words starting with Y, 6-letter words ending in Y and words with Y.