This problem would best be solved by graphing.  Since I don't know how to do graphing (is it even possible?) in the Wyzant Answers blank, I will explain what you will see...

After plotting the three points, you will see that the line from A to B is horizontal, since they have the same y coordinate.

You will also see that the line from B to C is vertical since they have the same x coordinate.

Since line segment AB is horizontal and line segment BC is vertical, they are perpendicular.

If two legs of a triangle are perpendicular, the triangle is a right triangle.

Let's find distance between the points, by using the formula d=√((x₁ - x₂)²+(y₁ - y₂)²) 

A(0 ,-6)    B(3 ,-6)      (x₁ - x₂)² = (0 - 3)² = (-3)² = 9 ,   (y₁ - y₂)² = (-6 - (-6))² = 0           
   x₁, y₁             x₂, y₂            
lABl = √(9+0) = 3 = a      
B(3, -6)     C(3, -2)     (x₁ - x₂)² = (3 - 3)² = 0 ,   (y₁ - y₂)² = (-6 - (-2))² = (-6 + 2)² = 16
   x₁, y₁             x₂, y₂
lBCl = √16 = 4 = b                   
A(0 ,-6)     C(3, -2)     (x₁ - x₂)² = (0 - 3)² = 9 ,  (y₁ - y₂)² = (-6 - (-2))² = (-6 + 2)² = 16
   x₁, y₁              x₂, y₂               
lACl = √(9+16) = 5 = c
                                c² = a² + b²   -----------> ΔABC is a right Δ

Well start off with a coordinate grid.  then add the dots and see if it is an acute triangle, obtuse triangle or right triangle.

A(0,-6) right 0 units and down 6 units

B(3,-6) right 3 units and down 6 units

C(3,-2) Right 3 units and down 2 units

connect the dots starting with A Going Right 3 units to B, From B to C you go Straight up 4 units to -2

The angle from A to B to C is a right angle. the triangle is a right triangle.

For extra credit use the Pythagorean Theorem to find the lengths of all three sides, You know from A to B is 3 units and from B to C is 4 units.

Pythagorean Theorem  is a^2 + B^2 = C^2   plug in 3 for A and 4 for B and solve the equation.