How many yards of concrete do you need for my project 6 feet by 6 feet and four inches deep?

That equates to 2 yards by 2 yards by 4/36 of a yard = 2 x 2 x 1/9 = 4/12 = 4/9 of a sq yard.

Therefore, by normally accepted trade measurements, you will need just under 1/2 yard of concrete.

A "yard" of concrete refers to a cubic yard which is 3 x 3 x 3 feet = 27 cubic feet.

Your project is 6 x 6 x 1/3 feet = 12 cubic feet or a bit less than 1/2 cubic yard, but more than 1/3.