What is 6 letter card game e a te?

The six-letter card game you're describing is likely "Euchre".

Euchre is a trick-taking card game that is popular in North America. It is played with a deck of 24 cards (9-Ace of each suit), and the goal is to win at least three out of five tricks.

Let me know if you have any other questions about Euchre!