Consider the region in the coordinate plane enclosed by the vertical lines x = -4 and x = 2 and the horizontal lines y = -2 and y = 3. What is the area of this region in square units?

Introduction / Context:
This problem asks you to find the area of a rectangular region defined in the coordinate plane by two vertical lines and two horizontal lines. It checks your understanding of how to interpret algebraic equations like x = constant and y = constant as vertical and horizontal boundaries, and then how to compute the area of the rectangle formed by those boundaries. Such coordinate geometry questions are common in aptitude and school level exams.

Given Data / Assumptions:

• The region is bounded on the left by the line x = -4.
• It is bounded on the right by the line x = 2.
• It is bounded below by the line y = -2.
• It is bounded above by the line y = 3.
• The shape enclosed by these four lines is a rectangle, and we must find its area in square units.

Concept / Approach:
The distance between two vertical lines x = a and x = b is |b − a|, and the distance between two horizontal lines y = c and y = d is |d − c|. These give the width and height of the rectangle in the coordinate plane. The area of the rectangle is then simply width * height. We will compute the horizontal length along the x axis and the vertical length along the y axis, and then multiply them to obtain the area.

Step-by-Step Solution:
Horizontal distance between x = -4 and x = 2 is |2 − (-4)| = |2 + 4| = 6 units.Vertical distance between y = -2 and y = 3 is |3 − (-2)| = |3 + 2| = 5 units.These distances form the sides of a rectangle with width 6 and height 5.Area of the rectangle = width * height = 6 * 5.Therefore, the area is 30 square units.

Verification / Alternative check:
You can visualise this region by sketching the lines on graph paper. Mark x = -4 and x = 2 as two vertical lines, and y = -2 and y = 3 as two horizontal lines. Their intersection points are the corners of a rectangle at (-4, -2), (-4, 3), (2, -2), and (2, 3). Counting grid squares or calculating the lengths along each axis both confirm that the rectangle is 6 units wide and 5 units tall, giving an area of 30 square units.

Why Other Options Are Wrong:
Option 12 likely comes from multiplying 6 by 2 instead of 6 by 5. Option 24 might arise from mixing one of the distances or misreading a boundary value. Option 15 is only half of the correct area and would correspond to width 3 and height 5 or similar confusion. Option 60 doubles the correct area and might result from mistakenly using 12 and 5 as dimensions. None of these match the correct rectangle formed by the given lines.

Common Pitfalls:
Learners sometimes misinterpret negative coordinates and treat -4 and 2 as a distance of 2, rather than 6. Another common mistake is to subtract the smaller from the larger without taking absolute value, but here that still gives the correct positive value if done correctly. Some also forget that area must be positive and might be unsure which value to subtract from which. Thinking in terms of absolute lengths between coordinates helps avoid these issues.

Final Answer:
The area of the enclosed region is 30 square units.