The image shows a rectangle ABCD, with diagonals intersecting at point E. The diagonals of a rectangle are congruent (i.e., they have the same length). In this case, the diagonals are $AC$ and $BD$. We are provided with algebraic expressions for parts of these diagonals:

• $AC = 8x - 12$
• $BD = 20$

Since the diagonals of a rectangle are congruent, we can set these two expressions equal to each other:

$8x - 12 = 20$

Now, let's solve for $x$:

1. Add 12 to both sides:

$8x = 32$

2. Divide both sides by 8:

$x = 4$

Thus, the value of $x$ is 4, which corresponds to option B.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. Why are the diagonals of a rectangle always congruent?
2. How would this problem change if it were a rhombus instead of a rectangle?
3. What other properties of diagonals are unique to rectangles?
4. How can we verify that the diagonals bisect each other in a rectangle?
5. What is the difference in diagonal properties between a rectangle and a general parallelogram?

Tip: In geometric problems involving diagonals, identifying congruent parts or relationships between angles can often simplify algebraic calculations.