For number 2, I've successfully graphed it but how do I go about finding its area of the shaded region?
That looks to me like a trapezoid. Do you know the formula for area of a trapezoid?
If not, notice that if you draw a line at y= 3, you divide this figure into a rectangle, with length 6 and height 3 and a right triangle with base 6 and height 2. Do you know how to find the area of a rectangle and triangle?