Final answer:
The correct expression for the area of a rectangle with a width of 6 inches and a coefficient increased by 2 is 8w square inches, which is not listed in the options provided, suggesting an error in the choices.
Step-by-step explanation:
The question asks for the expression for the area of a rectangle when the coefficient of its width (6 inches) increases by 2. To find this, we consider that the area of a rectangle is given by length × width. If the width is 6 inches and the coefficient increases by 2, then the new coefficient is 6 + 2, which equals 8. Therefore, if we let 'w' represent the length, the new area expression with the increased coefficient would be 8 × w, which can be written as 8w square inches. None of the options A) 18w sq in., B) OOO 40 + 12 sq in., C) 12w sq in., D) 6w + 12 sq in. match the correct expression; hence, there seems to be an error in the provided choices.