What is the number of square units in the area of trapezoid abcd with vertices a(0,0), b(0,-2), c(4,0), and d(4,6)?

The number of square units is what called "area" . The area of a trapezoid can be computed as :

where b is the length of the short basis, B is the length of the long basis and h is the Height. 
If you place the vertices of the trapezoid, you'll notice that b=2, B=6 and H=4. 
Is it clear to you ? 

First, take the GCF of all of the values

12x^4 + 39x^3 + 9x^2
3x^2( 4x^2 + 13x + 3)

Multiply the 'a' and 'c' values (4 and 3) to make factoring easier

4 X 3 = 12

Which two numbers multiply to get 12 and add to get 13? 1 and 12. How can 4 be go into those 2 values? 3 X 4 = 12

3x^2 ( 4x + 1)( x + 3)
3x^2 (x + 3)(4x + 1)

Hope this helps!