What type of quadrilateral has the vertices A(3 , 6), B(3 , 3), C(6 , 3),and D(6 , 6)

It is a square.

Background:

With this, lets find the distance between each of the shape's points, in order to find which shape it is.

Here's the distance formula, its a bit overkill for what you're doing right now, but it may help you with questions later on.

d=√(x2​−x1​)2+(y2​−y1​)2

Process:

​So with this, compare the distance between each of the points. With Point A, it is (3, 6) with Point B it is (3,3). The change between these two points is down 3.

Next, with Point B (3,3) and Point C (6,3). The change between these two points is right 3.

Then, with Point C (6,3) and Point D (6,6). The change between these two points is up 3.

Last, with Point D (6,6) and Point A (3,6). The change between these two points is left 3.

Reasoning:

From this, we can see that all of the distance lengths are 3 units and that each of them create 90 degree angle turns*.

*You can find this by noting that the total amount of a rotation is 360 degrees, so when you change walking from up to the right, you are turning 90 degrees to do so.

With this information in mind, it can be named a square given the definition of square:

"A regular quadrilateral, which means that it has four equal sides and four equal angles."

https://en.wikipedia.org/wiki/Square