what is the name of the figure that is 36 inches around and that has equal sides, each 6 inches long?

is it a hexagon?

Right.

By "around" do you mean perimeter?

A six figured polygon with equal sides, is called a regular hexagon.

The figure you are describing is a circle. The fact that it has a circumference of 36 inches tells us that the distance around the circle, or its perimeter, is 36 inches. Since all sides of a circle are equal, we can conclude that the diameter of the circle is also 6 inches.