Given:
log2(4x + 1) * log2(4x - 1) = log2 8

To find the value of x, we need to solve the given equation. Let's break down the problem into smaller steps to understand the solution.

Step 1: Simplify the equation
Using the property of logarithms, we can rewrite the equation as:
log2((4x + 1) * (4x - 1)) = log2 8

Step 2: Simplify the right side of the equation
Since log2 8 is equal to log2(2^3), we can simplify it further:
log2((4x + 1) * (4x - 1)) = log2(2^3)

Step 3: Apply the property of logarithms
According to the property loga(b * c) = loga(b) + loga(c), we can rewrite the left side of the equation as:
log2(4x + 1) + log2(4x - 1) = log2(2^3)

Step 4: Simplify the right side of the equation
Since 2^3 is equal to 8, we can further simplify the equation:
log2(4x + 1) + log2(4x - 1) = log2 8

Step 5: Apply the property of logarithms
According to the property loga(b) + loga(c) = loga(b * c), we can combine the logarithms on the left side of the equation:
log2((4x + 1) * (4x - 1)) = log2 8

Step 6: Cancel out the logarithms
Since log2((4x + 1) * (4x - 1)) = log2 8, we can conclude that
(4x + 1) * (4x - 1) = 8

Step 7: Solve the equation
Expanding the equation (4x + 1) * (4x - 1) = 8, we get:
16x^2 - 1 = 8

Rearranging the equation, we have:
16x^2 = 9

Step 8: Find the value of x
Dividing both sides of the equation by 16, we get:
x^2 = 9/16

Taking the square root of both sides, we have:
x = ±√(9/16)

Since x cannot be negative, we take the positive square root:
x = √(9/16)

Simplifying the square root, we get:
x = 3/4

Therefore, the value of x is 3/4, which is equivalent to 0.75.

Hence, the correct answer is option B) 0.