If a 20 in. by 30in. picture has a wooden frame "x" in. wide surrounding it, wich equation can be used to find the total area of the picture frame?

The area of the PICTURE is, indeed, 20 x 30 = 600 square inches. But the frame surrounds the picture, and the width of the strips making up the frame is x (see diagram).

The width of the picture frame is 20 + 2x (the width of the picture plus two strips of frame).
The length of the picture frame is 30 + 2x (the length of the picture plus two strips of frame.

The area of the frame is (20 + 2x)(30 + 3x). To get the area of JUST the frame, subtract out the area of the picture. You get (20 + 2x)(30 + 2x) - 600.

This isn't really an equation; it's an expression, and it could be written in a different form by multiplying the two binomials out and simplifying.

I have assumed that the 20 in and 30 in measurements give the size of the picture INSIDE the frame!